LMFDB - Space of modular forms of level 35700, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 35700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	35700.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 93 $
Sturm bound:			$17280$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(35700))$.

	Total	New	Old
Modular forms	8712	304	8408
Cusp forms	8569	304	8265
Eisenstein series	143	0	143

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$2$	$3$	$5$	$7$	$17$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$7$	$17$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$+$	$252$	$0$	$252$	$247$	$0$	$247$	$5$	$0$	$5$
$+$	$+$	$+$	$+$	$-$	$-$	$291$	$0$	$291$	$285$	$0$	$285$	$6$	$0$	$6$
$+$	$+$	$+$	$-$	$+$	$-$	$288$	$0$	$288$	$282$	$0$	$282$	$6$	$0$	$6$
$+$	$+$	$+$	$-$	$-$	$+$	$261$	$0$	$261$	$255$	$0$	$255$	$6$	$0$	$6$
$+$	$+$	$-$	$+$	$+$	$-$	$283$	$0$	$283$	$277$	$0$	$277$	$6$	$0$	$6$
$+$	$+$	$-$	$+$	$-$	$+$	$264$	$0$	$264$	$258$	$0$	$258$	$6$	$0$	$6$
$+$	$+$	$-$	$-$	$+$	$+$	$269$	$0$	$269$	$263$	$0$	$263$	$6$	$0$	$6$
$+$	$+$	$-$	$-$	$-$	$-$	$276$	$0$	$276$	$270$	$0$	$270$	$6$	$0$	$6$
$+$	$-$	$+$	$+$	$+$	$-$	$258$	$0$	$258$	$252$	$0$	$252$	$6$	$0$	$6$
$+$	$-$	$+$	$+$	$-$	$+$	$291$	$0$	$291$	$285$	$0$	$285$	$6$	$0$	$6$
$+$	$-$	$+$	$-$	$+$	$+$	$282$	$0$	$282$	$276$	$0$	$276$	$6$	$0$	$6$
$+$	$-$	$+$	$-$	$-$	$-$	$261$	$0$	$261$	$255$	$0$	$255$	$6$	$0$	$6$
$+$	$-$	$-$	$+$	$+$	$+$	$279$	$0$	$279$	$273$	$0$	$273$	$6$	$0$	$6$
$+$	$-$	$-$	$+$	$-$	$-$	$266$	$0$	$266$	$260$	$0$	$260$	$6$	$0$	$6$
$+$	$-$	$-$	$-$	$+$	$-$	$273$	$0$	$273$	$267$	$0$	$267$	$6$	$0$	$6$
$+$	$-$	$-$	$-$	$-$	$+$	$274$	$0$	$274$	$268$	$0$	$268$	$6$	$0$	$6$
$-$	$+$	$+$	$+$	$+$	$-$	$270$	$19$	$251$	$267$	$19$	$248$	$3$	$0$	$3$
$-$	$+$	$+$	$+$	$-$	$+$	$276$	$17$	$259$	$273$	$17$	$256$	$3$	$0$	$3$
$-$	$+$	$+$	$-$	$+$	$+$	$279$	$16$	$263$	$276$	$16$	$260$	$3$	$0$	$3$
$-$	$+$	$+$	$-$	$-$	$-$	$261$	$20$	$241$	$258$	$20$	$238$	$3$	$0$	$3$
$-$	$+$	$-$	$+$	$+$	$+$	$269$	$20$	$249$	$266$	$20$	$246$	$3$	$0$	$3$
$-$	$+$	$-$	$+$	$-$	$-$	$273$	$20$	$253$	$270$	$20$	$250$	$3$	$0$	$3$
$-$	$+$	$-$	$-$	$+$	$-$	$268$	$22$	$246$	$265$	$22$	$243$	$3$	$0$	$3$
$-$	$+$	$-$	$-$	$-$	$+$	$276$	$18$	$258$	$273$	$18$	$255$	$3$	$0$	$3$
$-$	$-$	$+$	$+$	$+$	$+$	$264$	$17$	$247$	$261$	$17$	$244$	$3$	$0$	$3$
$-$	$-$	$+$	$+$	$-$	$-$	$276$	$19$	$257$	$273$	$19$	$254$	$3$	$0$	$3$
$-$	$-$	$+$	$-$	$+$	$-$	$285$	$20$	$265$	$282$	$20$	$262$	$3$	$0$	$3$
$-$	$-$	$+$	$-$	$-$	$+$	$261$	$16$	$245$	$258$	$16$	$242$	$3$	$0$	$3$
$-$	$-$	$-$	$+$	$+$	$-$	$273$	$20$	$253$	$270$	$20$	$250$	$3$	$0$	$3$
$-$	$-$	$-$	$+$	$-$	$+$	$271$	$20$	$251$	$268$	$20$	$248$	$3$	$0$	$3$
$-$	$-$	$-$	$-$	$+$	$+$	$264$	$18$	$246$	$261$	$18$	$243$	$3$	$0$	$3$
$-$	$-$	$-$	$-$	$-$	$-$	$278$	$22$	$256$	$275$	$22$	$253$	$3$	$0$	$3$
Plus space					$+$	$4332$	$142$	$4190$	$4261$	$142$	$4119$	$71$	$0$	$71$
Minus space					$-$	$4380$	$162$	$4218$	$4308$	$162$	$4146$	$72$	$0$	$72$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(35700))$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				A-L signs					Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	7	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
35700.2.a.a	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots$
35700.2.a.b	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-4q^{11}-q^{17}-4q^{19}+\cdots$
35700.2.a.c	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$
35700.2.a.d	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-3q^{11}+q^{13}-q^{17}+\cdots$
35700.2.a.e	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-3q^{11}+6q^{13}+\cdots$
35700.2.a.f	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
35700.2.a.g	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
35700.2.a.h	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-6q^{13}-q^{17}+6q^{19}+\cdots$
35700.2.a.i	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{13}+q^{17}+2q^{19}+\cdots$
35700.2.a.j	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+q^{13}-q^{17}+8q^{19}+\cdots$
35700.2.a.k	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+2q^{13}+q^{17}+6q^{19}+\cdots$
35700.2.a.l	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+4q^{13}-q^{17}-8q^{19}+\cdots$
35700.2.a.m	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+4q^{13}-q^{17}-4q^{19}+\cdots$
35700.2.a.n	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+4q^{13}+q^{17}-4q^{19}+\cdots$
35700.2.a.o	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+q^{11}-4q^{13}+q^{17}+\cdots$
35700.2.a.p	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+3q^{11}-2q^{13}+\cdots$
35700.2.a.q	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
35700.2.a.r	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$
35700.2.a.s	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{11}-q^{17}-2q^{19}+\cdots$
35700.2.a.t	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+4q^{13}+q^{17}-4q^{19}+\cdots$
35700.2.a.u	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+6q^{13}-q^{17}-2q^{19}+\cdots$
35700.2.a.v	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots$
35700.2.a.w	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+3q^{11}-q^{17}-2q^{19}+\cdots$
35700.2.a.x	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
35700.2.a.y	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
35700.2.a.z	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots$
35700.2.a.ba	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$
35700.2.a.bb	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
35700.2.a.bc	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-q^{11}+7q^{13}+q^{17}+\cdots$
35700.2.a.bd	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{13}-q^{17}-4q^{19}+\cdots$
35700.2.a.be	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots$
35700.2.a.bf	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+2q^{11}-q^{17}-6q^{19}+\cdots$
35700.2.a.bg	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+2q^{11}+5q^{13}+\cdots$
35700.2.a.bh	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+3q^{11}+q^{17}-2q^{19}+\cdots$
35700.2.a.bi	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
35700.2.a.bj	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
35700.2.a.bk	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-5q^{11}-2q^{13}+\cdots$
35700.2.a.bl	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-5q^{11}-q^{13}+q^{17}+\cdots$
35700.2.a.bm	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$
35700.2.a.bn	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
35700.2.a.bo	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-3q^{11}-6q^{13}+\cdots$
35700.2.a.bp	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
35700.2.a.bq	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-2q^{11}-q^{13}+q^{17}+\cdots$
35700.2.a.br	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-6q^{13}+q^{17}-2q^{19}+\cdots$
35700.2.a.bs	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-4q^{13}+q^{17}-8q^{19}+\cdots$
35700.2.a.bt	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-q^{13}+q^{17}+8q^{19}+\cdots$
35700.2.a.bu	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+q^{11}+4q^{13}-q^{17}+\cdots$
35700.2.a.bv	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
35700.2.a.bw	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots$
35700.2.a.bx	$35700$	$2$	35700.a	1.a	$1$	$1$	$1$	$285.066$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
35700.2.a.by	$35700$	$2$	35700.a	1.a	$1$	$2$	$2$	$285.066$	$\Q(\sqrt{13}) $	None	✓	?				$-1$		$0$	$-2$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
35700.2.a.bz	$35700$	$2$	35700.a	1.a	$1$	$2$	$2$	$285.066$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$0$	$-2$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
35700.2.a.ca	$35700$	$2$	35700.a	1.a	$1$	$2$	$2$	$285.066$	$\Q(\sqrt{10}) $	None	✓	?				$-1$		$0$	$-2$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
35700.2.a.cb	$35700$	$2$	35700.a	1.a	$1$	$2$	$2$	$285.066$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$0$	$-2$	$0$	$2$	$-$	$+$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
35700.2.a.cc	$35700$	$2$	35700.a	1.a	$1$	$2$	$2$	$285.066$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$0$	$-2$	$0$	$2$	$-$	$+$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
35700.2.a.cd	$35700$	$2$	35700.a	1.a	$1$	$2$	$2$	$285.066$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
35700.2.a.ce	$35700$	$2$	35700.a	1.a	$1$	$2$	$2$	$285.066$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
35700.2.a.cf	$35700$	$2$	35700.a	1.a	$1$	$2$	$2$	$285.066$	$\Q(\sqrt{17}) $	None	✓	?				$-1$		$0$	$2$	$0$	$2$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
35700.2.a.cg	$35700$	$2$	35700.a	1.a	$1$	$2$	$2$	$285.066$	$\Q(\sqrt{13}) $	None	✓	?				$-1$		$0$	$2$	$0$	$2$	$-$	$-$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
35700.2.a.ch	$35700$	$2$	35700.a	1.a	$1$	$2$	$2$	$285.066$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$0$	$2$	$0$	$2$	$-$	$-$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
35700.2.a.ci	$35700$	$2$	35700.a	1.a	$1$	$2$	$2$	$285.066$	$\Q(\sqrt{3}) $	None	✓	?				$-1$		$0$	$2$	$0$	$2$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
35700.2.a.cj	$35700$	$2$	35700.a	1.a	$1$	$3$	$3$	$285.066$	3.3.4764.1	None	✓	?				$-1$		$0$	$3$	$0$	$-3$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
35700.2.a.ck	$35700$	$2$	35700.a	1.a	$1$	$3$	$3$	$285.066$	$\Q(\zeta_{18})^+$	None	✓	?				$-1$		$0$	$3$	$0$	$-3$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
35700.2.a.cl	$35700$	$2$	35700.a	1.a	$1$	$4$	$4$	$285.066$	4.4.20308.1	None	✓	?				$-1$		$0$	$-4$	$0$	$4$	$-$	$+$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
35700.2.a.cm	$35700$	$2$	35700.a	1.a	$1$	$4$	$4$	$285.066$	4.4.7168.1	None	✓	?				$-1$		$0$	$-4$	$0$	$4$	$-$	$+$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
35700.2.a.cn	$35700$	$2$	35700.a	1.a	$1$	$5$	$5$	$285.066$	5.5.712753.1	None	✓	?	✓			$-1$		$0$	$-5$	$0$	$-5$	$-$	$+$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
35700.2.a.co	$35700$	$2$	35700.a	1.a	$1$	$5$	$5$	$285.066$	5.5.236549.1	None	✓	?				$-1$		$0$	$-5$	$0$	$5$	$-$	$+$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
35700.2.a.cp	$35700$	$2$	35700.a	1.a	$1$	$5$	$5$	$285.066$	5.5.7197952.1	None	✓	?				$-1$		$0$	$5$	$0$	$-5$	$-$	$-$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
35700.2.a.cq	$35700$	$2$	35700.a	1.a	$1$	$5$	$5$	$285.066$	5.5.712753.1	None	✓	?				$-1$		$0$	$5$	$0$	$5$	$-$	$-$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
35700.2.a.cr	$35700$	$2$	35700.a	1.a	$1$	$6$	$6$	$285.066$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	?				$-1$		$0$	$-6$	$0$	$-6$	$-$	$+$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
35700.2.a.cs	$35700$	$2$	35700.a	1.a	$1$	$6$	$6$	$285.066$	6.6.202392513.1	None	✓	?				$-1$		$0$	$-6$	$0$	$-6$	$-$	$+$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
35700.2.a.ct	$35700$	$2$	35700.a	1.a	$1$	$6$	$6$	$285.066$	6.6.331376345.1	None	✓	?	✓			$-1$		$0$	$-6$	$0$	$6$	$-$	$+$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
35700.2.a.cu	$35700$	$2$	35700.a	1.a	$1$	$6$	$6$	$285.066$	6.6.331376345.1	None	✓	?				$-1$		$0$	$6$	$0$	$-6$	$-$	$-$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
35700.2.a.cv	$35700$	$2$	35700.a	1.a	$1$	$6$	$6$	$285.066$	6.6.137521152.1	None	✓	?				$-1$		$0$	$6$	$0$	$6$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
35700.2.a.cw	$35700$	$2$	35700.a	1.a	$1$	$6$	$6$	$285.066$	6.6.202392513.1	None	✓	?	✓			$-1$		$0$	$6$	$0$	$6$	$-$	$-$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
35700.2.a.cx	$35700$	$2$	35700.a	1.a	$1$	$7$	$7$	$285.066$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?				$-1$		$0$	$-7$	$0$	$-7$	$-$	$+$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
35700.2.a.cy	$35700$	$2$	35700.a	1.a	$1$	$7$	$7$	$285.066$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?				$-1$		$0$	$-7$	$0$	$7$	$-$	$+$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
35700.2.a.cz	$35700$	$2$	35700.a	1.a	$1$	$7$	$7$	$285.066$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?	✓			$-1$		$0$	$7$	$0$	$-7$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
35700.2.a.da	$35700$	$2$	35700.a	1.a	$1$	$7$	$7$	$285.066$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?	✓			$-1$		$0$	$7$	$0$	$7$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
35700.2.a.db	$35700$	$2$	35700.a	1.a	$1$	$8$	$8$	$285.066$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?				$-1$		$0$	$-8$	$0$	$8$	$-$	$+$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
35700.2.a.dc	$35700$	$2$	35700.a	1.a	$1$	$8$	$8$	$285.066$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?	✓			$-1$		$0$	$8$	$0$	$-8$	$-$	$-$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
35700.2.a.dd	$35700$	$2$	35700.a	1.a	$1$	$9$	$9$	$285.066$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-9$	$0$	$-9$	$-$	$+$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
35700.2.a.de	$35700$	$2$	35700.a	1.a	$1$	$9$	$9$	$285.066$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-9$	$0$	$9$	$-$	$+$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
35700.2.a.df	$35700$	$2$	35700.a	1.a	$1$	$9$	$9$	$285.066$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?				$-1$		$0$	$9$	$0$	$-9$	$-$	$-$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
35700.2.a.dg	$35700$	$2$	35700.a	1.a	$1$	$9$	$9$	$285.066$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?				$-1$		$0$	$9$	$0$	$9$	$-$	$-$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
35700.2.a.dh	$35700$	$2$	35700.a	1.a	$1$	$10$	$10$	$285.066$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-10$	$0$	$-10$	$-$	$+$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
35700.2.a.di	$35700$	$2$	35700.a	1.a	$1$	$10$	$10$	$285.066$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-10$	$0$	$10$	$-$	$+$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
35700.2.a.dj	$35700$	$2$	35700.a	1.a	$1$	$10$	$10$	$285.066$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-10$	$0$	$10$	$-$	$+$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
35700.2.a.dk	$35700$	$2$	35700.a	1.a	$1$	$10$	$10$	$285.066$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	?	✓			$-1$		$0$	$10$	$0$	$-10$	$-$	$-$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
35700.2.a.dl	$35700$	$2$	35700.a	1.a	$1$	$10$	$10$	$285.066$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	?	✓			$-1$		$0$	$10$	$0$	$-10$	$-$	$-$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
35700.2.a.dm	$35700$	$2$	35700.a	1.a	$1$	$10$	$10$	$285.066$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	?	✓			$-1$		$0$	$10$	$0$	$10$	$-$	$-$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
35700.2.a.dn	$35700$	$2$	35700.a	1.a	$1$	$11$	$11$	$285.066$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-11$	$0$	$-11$	$-$	$+$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
35700.2.a.do	$35700$	$2$	35700.a	1.a	$1$	$11$	$11$	$285.066$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	?	✓			$-1$		$0$	$11$	$0$	$11$	$-$	$-$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(35700))$ into lower level spaces

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 35700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	35700.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 93 \)
Sturm bound:			\(17280\)

\(2\)	\(3\)	\(5\)	\(7\)	\(17\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(7\)	\(17\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(252\)	\(0\)	\(252\)	\(247\)	\(0\)	\(247\)	\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(291\)	\(0\)	\(291\)	\(285\)	\(0\)	\(285\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(288\)	\(0\)	\(288\)	\(282\)	\(0\)	\(282\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(261\)	\(0\)	\(261\)	\(255\)	\(0\)	\(255\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(283\)	\(0\)	\(283\)	\(277\)	\(0\)	\(277\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(264\)	\(0\)	\(264\)	\(258\)	\(0\)	\(258\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(269\)	\(0\)	\(269\)	\(263\)	\(0\)	\(263\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(276\)	\(0\)	\(276\)	\(270\)	\(0\)	\(270\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(258\)	\(0\)	\(258\)	\(252\)	\(0\)	\(252\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(291\)	\(0\)	\(291\)	\(285\)	\(0\)	\(285\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(282\)	\(0\)	\(282\)	\(276\)	\(0\)	\(276\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(261\)	\(0\)	\(261\)	\(255\)	\(0\)	\(255\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(279\)	\(0\)	\(279\)	\(273\)	\(0\)	\(273\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(266\)	\(0\)	\(266\)	\(260\)	\(0\)	\(260\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(273\)	\(0\)	\(273\)	\(267\)	\(0\)	\(267\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(274\)	\(0\)	\(274\)	\(268\)	\(0\)	\(268\)	\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(270\)	\(19\)	\(251\)	\(267\)	\(19\)	\(248\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(276\)	\(17\)	\(259\)	\(273\)	\(17\)	\(256\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(279\)	\(16\)	\(263\)	\(276\)	\(16\)	\(260\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(261\)	\(20\)	\(241\)	\(258\)	\(20\)	\(238\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(269\)	\(20\)	\(249\)	\(266\)	\(20\)	\(246\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(273\)	\(20\)	\(253\)	\(270\)	\(20\)	\(250\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(268\)	\(22\)	\(246\)	\(265\)	\(22\)	\(243\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(276\)	\(18\)	\(258\)	\(273\)	\(18\)	\(255\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(264\)	\(17\)	\(247\)	\(261\)	\(17\)	\(244\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(276\)	\(19\)	\(257\)	\(273\)	\(19\)	\(254\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(285\)	\(20\)	\(265\)	\(282\)	\(20\)	\(262\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(261\)	\(16\)	\(245\)	\(258\)	\(16\)	\(242\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(273\)	\(20\)	\(253\)	\(270\)	\(20\)	\(250\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(271\)	\(20\)	\(251\)	\(268\)	\(20\)	\(248\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(264\)	\(18\)	\(246\)	\(261\)	\(18\)	\(243\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(278\)	\(22\)	\(256\)	\(275\)	\(22\)	\(253\)	\(3\)	\(0\)	\(3\)
Plus space					\(+\)	\(4332\)	\(142\)	\(4190\)	\(4261\)	\(142\)	\(4119\)	\(71\)	\(0\)	\(71\)
Minus space					\(-\)	\(4380\)	\(162\)	\(4218\)	\(4308\)	\(162\)	\(4146\)	\(72\)	\(0\)	\(72\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(35700))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(35700))\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	35700.2.a
Level	$35700$
Weight	$2$
Character orbit	35700.a
Rep. character	$\chi_{35700}(1,\cdot)$
Character field	$\Q$
Dimension	$304$
Newform subspaces	$93$
Sturm bound	$17280$