LMFDB - Space of modular forms of level 27300, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 27300 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	27300.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 69 $
Sturm bound:			$13440$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(27300))$.

	Total	New	Old
Modular forms	6792	228	6564
Cusp forms	6649	228	6421
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.

$2$	$3$	$5$	$7$	$13$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$7$	$13$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$+$	$210$	$0$	$210$	$205$	$0$	$205$	$5$	$0$	$5$
$+$	$+$	$+$	$+$	$-$	$-$	$213$	$0$	$213$	$207$	$0$	$207$	$6$	$0$	$6$
$+$	$+$	$+$	$-$	$+$	$-$	$213$	$0$	$213$	$207$	$0$	$207$	$6$	$0$	$6$
$+$	$+$	$+$	$-$	$-$	$+$	$210$	$0$	$210$	$204$	$0$	$204$	$6$	$0$	$6$
$+$	$+$	$-$	$+$	$+$	$-$	$216$	$0$	$216$	$210$	$0$	$210$	$6$	$0$	$6$
$+$	$+$	$-$	$+$	$-$	$+$	$213$	$0$	$213$	$207$	$0$	$207$	$6$	$0$	$6$
$+$	$+$	$-$	$-$	$+$	$+$	$213$	$0$	$213$	$207$	$0$	$207$	$6$	$0$	$6$
$+$	$+$	$-$	$-$	$-$	$-$	$216$	$0$	$216$	$210$	$0$	$210$	$6$	$0$	$6$
$+$	$-$	$+$	$+$	$+$	$-$	$216$	$0$	$216$	$210$	$0$	$210$	$6$	$0$	$6$
$+$	$-$	$+$	$+$	$-$	$+$	$213$	$0$	$213$	$207$	$0$	$207$	$6$	$0$	$6$
$+$	$-$	$+$	$-$	$+$	$+$	$213$	$0$	$213$	$207$	$0$	$207$	$6$	$0$	$6$
$+$	$-$	$+$	$-$	$-$	$-$	$216$	$0$	$216$	$210$	$0$	$210$	$6$	$0$	$6$
$+$	$-$	$-$	$+$	$+$	$+$	$210$	$0$	$210$	$204$	$0$	$204$	$6$	$0$	$6$
$+$	$-$	$-$	$+$	$-$	$-$	$213$	$0$	$213$	$207$	$0$	$207$	$6$	$0$	$6$
$+$	$-$	$-$	$-$	$+$	$-$	$213$	$0$	$213$	$207$	$0$	$207$	$6$	$0$	$6$
$+$	$-$	$-$	$-$	$-$	$+$	$210$	$0$	$210$	$204$	$0$	$204$	$6$	$0$	$6$
$-$	$+$	$+$	$+$	$+$	$-$	$213$	$14$	$199$	$210$	$14$	$196$	$3$	$0$	$3$
$-$	$+$	$+$	$+$	$-$	$+$	$210$	$12$	$198$	$207$	$12$	$195$	$3$	$0$	$3$
$-$	$+$	$+$	$-$	$+$	$+$	$210$	$13$	$197$	$207$	$13$	$194$	$3$	$0$	$3$
$-$	$+$	$+$	$-$	$-$	$-$	$213$	$15$	$198$	$210$	$15$	$195$	$3$	$0$	$3$
$-$	$+$	$-$	$+$	$+$	$+$	$210$	$16$	$194$	$207$	$16$	$191$	$3$	$0$	$3$
$-$	$+$	$-$	$+$	$-$	$-$	$213$	$16$	$197$	$210$	$16$	$194$	$3$	$0$	$3$
$-$	$+$	$-$	$-$	$+$	$-$	$213$	$14$	$199$	$210$	$14$	$196$	$3$	$0$	$3$
$-$	$+$	$-$	$-$	$-$	$+$	$210$	$14$	$196$	$207$	$14$	$193$	$3$	$0$	$3$
$-$	$-$	$+$	$+$	$+$	$+$	$210$	$12$	$198$	$207$	$12$	$195$	$3$	$0$	$3$
$-$	$-$	$+$	$+$	$-$	$-$	$213$	$16$	$197$	$210$	$16$	$194$	$3$	$0$	$3$
$-$	$-$	$+$	$-$	$+$	$-$	$213$	$15$	$198$	$210$	$15$	$195$	$3$	$0$	$3$
$-$	$-$	$+$	$-$	$-$	$+$	$210$	$11$	$199$	$207$	$11$	$196$	$3$	$0$	$3$
$-$	$-$	$-$	$+$	$+$	$-$	$213$	$16$	$197$	$210$	$16$	$194$	$3$	$0$	$3$
$-$	$-$	$-$	$+$	$-$	$+$	$210$	$12$	$198$	$207$	$12$	$195$	$3$	$0$	$3$
$-$	$-$	$-$	$-$	$+$	$+$	$210$	$14$	$196$	$207$	$14$	$193$	$3$	$0$	$3$
$-$	$-$	$-$	$-$	$-$	$-$	$213$	$18$	$195$	$210$	$18$	$192$	$3$	$0$	$3$
Plus space					$+$	$3372$	$104$	$3268$	$3301$	$104$	$3197$	$71$	$0$	$71$
Minus space					$-$	$3420$	$124$	$3296$	$3348$	$124$	$3224$	$72$	$0$	$72$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(27300))$ 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	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
27300.2.a.a	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-5q^{11}-q^{13}+4q^{17}+\cdots$
27300.2.a.b	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-q^{13}-6q^{17}-4q^{19}+\cdots$
27300.2.a.c	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-q^{13}-4q^{19}+q^{21}+\cdots$
27300.2.a.d	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-q^{13}+3q^{17}+2q^{19}+\cdots$
27300.2.a.e	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+q^{13}-2q^{17}-8q^{19}+\cdots$
27300.2.a.f	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-5q^{11}-q^{13}-4q^{17}+\cdots$
27300.2.a.g	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-5q^{11}+q^{13}+4q^{19}+\cdots$
27300.2.a.h	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}+q^{13}-2q^{17}+\cdots$
27300.2.a.i	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}+q^{13}+6q^{17}+\cdots$
27300.2.a.j	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}+q^{13}+7q^{17}+\cdots$
27300.2.a.k	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+q^{13}+4q^{17}-8q^{19}+\cdots$
27300.2.a.l	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-6q^{11}+q^{13}+8q^{17}+\cdots$
27300.2.a.m	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-5q^{11}-q^{13}+4q^{19}+\cdots$
27300.2.a.n	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-5q^{11}+q^{13}+4q^{17}+\cdots$
27300.2.a.o	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{11}-q^{13}-7q^{17}+\cdots$
27300.2.a.p	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{11}-q^{13}+2q^{17}+\cdots$
27300.2.a.q	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+q^{13}-4q^{17}-q^{21}+\cdots$
27300.2.a.r	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+4q^{11}+q^{13}-2q^{17}+\cdots$
27300.2.a.s	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+4q^{11}+q^{13}+4q^{17}+\cdots$
27300.2.a.t	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-5q^{11}+q^{13}-4q^{17}+\cdots$
27300.2.a.u	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-2q^{11}+q^{13}-4q^{17}+\cdots$
27300.2.a.v	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+q^{13}-3q^{17}+2q^{19}+\cdots$
27300.2.a.w	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+2q^{11}-q^{13}+4q^{17}+\cdots$
27300.2.a.x	$27300$	$2$	27300.a	1.a	$1$	$1$	$1$	$217.992$	$\Q$	None	✓	?				$-1$		$0$	$1$	$0$	$1$	$-$	$-$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+4q^{11}-q^{13}-8q^{17}+\cdots$
27300.2.a.y	$27300$	$2$	27300.a	1.a	$1$	$2$	$2$	$217.992$	$\Q(\sqrt{13}) $	None	✓	?				$-1$		$0$	$-2$	$0$	$-2$	$-$	$+$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
27300.2.a.z	$27300$	$2$	27300.a	1.a	$1$	$2$	$2$	$217.992$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$0$	$-2$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
27300.2.a.ba	$27300$	$2$	27300.a	1.a	$1$	$2$	$2$	$217.992$	$\Q(\sqrt{21}) $	None	✓	?				$-1$		$0$	$-2$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
27300.2.a.bb	$27300$	$2$	27300.a	1.a	$1$	$2$	$2$	$217.992$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$0$	$-2$	$0$	$-2$	$-$	$+$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.bc	$27300$	$2$	27300.a	1.a	$1$	$2$	$2$	$217.992$	$\Q(\sqrt{33}) $	None	✓	?				$-1$		$0$	$-2$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
27300.2.a.bd	$27300$	$2$	27300.a	1.a	$1$	$2$	$2$	$217.992$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$0$	$-2$	$0$	$2$	$-$	$+$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.be	$27300$	$2$	27300.a	1.a	$1$	$2$	$2$	$217.992$	$\Q(\sqrt{5}) $	None	✓	?				$-1$		$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.bf	$27300$	$2$	27300.a	1.a	$1$	$2$	$2$	$217.992$	$\Q(\sqrt{37}) $	None	✓	?				$-1$		$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
27300.2.a.bg	$27300$	$2$	27300.a	1.a	$1$	$2$	$2$	$217.992$	$\Q(\sqrt{21}) $	None	✓	?				$-1$		$0$	$2$	$0$	$-2$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.bh	$27300$	$2$	27300.a	1.a	$1$	$2$	$2$	$217.992$	$\Q(\sqrt{13}) $	None	✓	?				$-1$		$0$	$2$	$0$	$2$	$-$	$-$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
27300.2.a.bi	$27300$	$2$	27300.a	1.a	$1$	$2$	$2$	$217.992$	$\Q(\sqrt{2}) $	None	✓	?				$-1$		$0$	$2$	$0$	$2$	$-$	$-$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
27300.2.a.bj	$27300$	$2$	27300.a	1.a	$1$	$3$	$3$	$217.992$	3.3.1229.1	None	✓	?				$-1$		$0$	$-3$	$0$	$-3$	$-$	$+$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
27300.2.a.bk	$27300$	$2$	27300.a	1.a	$1$	$3$	$3$	$217.992$	3.3.1373.1	None	✓	?				$-1$		$0$	$-3$	$0$	$3$	$-$	$+$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.bl	$27300$	$2$	27300.a	1.a	$1$	$3$	$3$	$217.992$	3.3.229.1	None	✓	?				$-1$		$0$	$-3$	$0$	$3$	$-$	$+$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.bm	$27300$	$2$	27300.a	1.a	$1$	$3$	$3$	$217.992$	3.3.2429.1	None	✓	?				$-1$		$0$	$-3$	$0$	$3$	$-$	$+$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
27300.2.a.bn	$27300$	$2$	27300.a	1.a	$1$	$3$	$3$	$217.992$	3.3.1101.1	None	✓	?				$-1$		$0$	$-3$	$0$	$3$	$-$	$+$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
27300.2.a.bo	$27300$	$2$	27300.a	1.a	$1$	$3$	$3$	$217.992$	3.3.3957.1	None	✓	?				$-1$		$0$	$3$	$0$	$-3$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.bp	$27300$	$2$	27300.a	1.a	$1$	$3$	$3$	$217.992$	3.3.5637.1	None	✓	?				$-1$		$0$	$3$	$0$	$-3$	$-$	$-$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
27300.2.a.bq	$27300$	$2$	27300.a	1.a	$1$	$3$	$3$	$217.992$	3.3.10997.1	None	✓	?				$-1$		$0$	$3$	$0$	$3$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
27300.2.a.br	$27300$	$2$	27300.a	1.a	$1$	$3$	$3$	$217.992$	3.3.1509.1	None	✓	?				$-1$		$0$	$3$	$0$	$3$	$-$	$-$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
27300.2.a.bs	$27300$	$2$	27300.a	1.a	$1$	$3$	$3$	$217.992$	3.3.837.1	None	✓	?				$-1$		$0$	$3$	$0$	$3$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
27300.2.a.bt	$27300$	$2$	27300.a	1.a	$1$	$4$	$4$	$217.992$	4.4.26541.1	None	✓	?				$-1$		$0$	$-4$	$0$	$-4$	$-$	$+$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.bu	$27300$	$2$	27300.a	1.a	$1$	$4$	$4$	$217.992$	4.4.238581.1	None	✓	?				$-1$		$0$	$-4$	$0$	$4$	$-$	$+$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
27300.2.a.bv	$27300$	$2$	27300.a	1.a	$1$	$4$	$4$	$217.992$	4.4.238581.1	None	✓	?	✓			$-1$		$0$	$4$	$0$	$-4$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.bw	$27300$	$2$	27300.a	1.a	$1$	$4$	$4$	$217.992$	4.4.26541.1	None	✓	?	✓			$-1$		$0$	$4$	$0$	$4$	$-$	$-$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
27300.2.a.bx	$27300$	$2$	27300.a	1.a	$1$	$5$	$5$	$217.992$	5.5.2027733.1	None	✓	?	✓			$-1$		$0$	$-5$	$0$	$-5$	$-$	$+$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
27300.2.a.by	$27300$	$2$	27300.a	1.a	$1$	$5$	$5$	$217.992$	5.5.4169021.1	None	✓	?	✓			$-1$		$0$	$-5$	$0$	$5$	$-$	$+$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.bz	$27300$	$2$	27300.a	1.a	$1$	$5$	$5$	$217.992$	5.5.4169021.1	None	✓	?				$-1$		$0$	$5$	$0$	$-5$	$-$	$-$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
27300.2.a.ca	$27300$	$2$	27300.a	1.a	$1$	$5$	$5$	$217.992$	5.5.2027733.1	None	✓	?				$-1$		$0$	$5$	$0$	$5$	$-$	$-$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.cb	$27300$	$2$	27300.a	1.a	$1$	$6$	$6$	$217.992$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-6$	$0$	$-6$	$-$	$+$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
27300.2.a.cc	$27300$	$2$	27300.a	1.a	$1$	$6$	$6$	$217.992$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	?				$-1$		$0$	$-6$	$0$	$6$	$-$	$+$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
27300.2.a.cd	$27300$	$2$	27300.a	1.a	$1$	$6$	$6$	$217.992$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-6$	$0$	$6$	$-$	$+$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
27300.2.a.ce	$27300$	$2$	27300.a	1.a	$1$	$6$	$6$	$217.992$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	?	✓			$-1$		$0$	$6$	$0$	$-6$	$-$	$-$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
27300.2.a.cf	$27300$	$2$	27300.a	1.a	$1$	$6$	$6$	$217.992$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	?				$-1$		$0$	$6$	$0$	$-6$	$-$	$-$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
27300.2.a.cg	$27300$	$2$	27300.a	1.a	$1$	$6$	$6$	$217.992$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	?				$-1$		$0$	$6$	$0$	$6$	$-$	$-$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
27300.2.a.ch	$27300$	$2$	27300.a	1.a	$1$	$7$	$7$	$217.992$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?				$-1$		$0$	$-7$	$0$	$-7$	$-$	$+$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
27300.2.a.ci	$27300$	$2$	27300.a	1.a	$1$	$7$	$7$	$217.992$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-7$	$0$	$7$	$-$	$+$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
27300.2.a.cj	$27300$	$2$	27300.a	1.a	$1$	$7$	$7$	$217.992$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?	✓			$-1$		$0$	$7$	$0$	$-7$	$-$	$-$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
27300.2.a.ck	$27300$	$2$	27300.a	1.a	$1$	$7$	$7$	$217.992$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	?	✓			$-1$		$0$	$7$	$0$	$7$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
27300.2.a.cl	$27300$	$2$	27300.a	1.a	$1$	$8$	$8$	$217.992$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-8$	$0$	$8$	$-$	$+$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
27300.2.a.cm	$27300$	$2$	27300.a	1.a	$1$	$8$	$8$	$217.992$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	?	✓			$-1$		$0$	$8$	$0$	$-8$	$-$	$-$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
27300.2.a.cn	$27300$	$2$	27300.a	1.a	$1$	$9$	$9$	$217.992$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-9$	$0$	$-9$	$-$	$+$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
27300.2.a.co	$27300$	$2$	27300.a	1.a	$1$	$9$	$9$	$217.992$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?	✓			$-1$		$0$	$-9$	$0$	$-9$	$-$	$+$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.cp	$27300$	$2$	27300.a	1.a	$1$	$9$	$9$	$217.992$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?	✓			$-1$		$0$	$9$	$0$	$9$	$-$	$-$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
27300.2.a.cq	$27300$	$2$	27300.a	1.a	$1$	$9$	$9$	$217.992$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	?	✓			$-1$		$0$	$9$	$0$	$9$	$-$	$-$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(27300))$ 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:	\( N \)	\(=\)	\( 27300 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	27300.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 69 \)
Sturm bound:			\(13440\)

\(2\)	\(3\)	\(5\)	\(7\)	\(13\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(7\)	\(13\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(210\)	\(0\)	\(210\)	\(205\)	\(0\)	\(205\)	\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(213\)	\(0\)	\(213\)	\(207\)	\(0\)	\(207\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(213\)	\(0\)	\(213\)	\(207\)	\(0\)	\(207\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(210\)	\(0\)	\(210\)	\(204\)	\(0\)	\(204\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(216\)	\(0\)	\(216\)	\(210\)	\(0\)	\(210\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(213\)	\(0\)	\(213\)	\(207\)	\(0\)	\(207\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(213\)	\(0\)	\(213\)	\(207\)	\(0\)	\(207\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(216\)	\(0\)	\(216\)	\(210\)	\(0\)	\(210\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(216\)	\(0\)	\(216\)	\(210\)	\(0\)	\(210\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(213\)	\(0\)	\(213\)	\(207\)	\(0\)	\(207\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(213\)	\(0\)	\(213\)	\(207\)	\(0\)	\(207\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(216\)	\(0\)	\(216\)	\(210\)	\(0\)	\(210\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(210\)	\(0\)	\(210\)	\(204\)	\(0\)	\(204\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(213\)	\(0\)	\(213\)	\(207\)	\(0\)	\(207\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(213\)	\(0\)	\(213\)	\(207\)	\(0\)	\(207\)	\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(210\)	\(0\)	\(210\)	\(204\)	\(0\)	\(204\)	\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(213\)	\(14\)	\(199\)	\(210\)	\(14\)	\(196\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(210\)	\(12\)	\(198\)	\(207\)	\(12\)	\(195\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(210\)	\(13\)	\(197\)	\(207\)	\(13\)	\(194\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(213\)	\(15\)	\(198\)	\(210\)	\(15\)	\(195\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(210\)	\(16\)	\(194\)	\(207\)	\(16\)	\(191\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(213\)	\(16\)	\(197\)	\(210\)	\(16\)	\(194\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(213\)	\(14\)	\(199\)	\(210\)	\(14\)	\(196\)	\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(210\)	\(14\)	\(196\)	\(207\)	\(14\)	\(193\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(210\)	\(12\)	\(198\)	\(207\)	\(12\)	\(195\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(213\)	\(16\)	\(197\)	\(210\)	\(16\)	\(194\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(213\)	\(15\)	\(198\)	\(210\)	\(15\)	\(195\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(210\)	\(11\)	\(199\)	\(207\)	\(11\)	\(196\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(213\)	\(16\)	\(197\)	\(210\)	\(16\)	\(194\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(210\)	\(12\)	\(198\)	\(207\)	\(12\)	\(195\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(210\)	\(14\)	\(196\)	\(207\)	\(14\)	\(193\)	\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(213\)	\(18\)	\(195\)	\(210\)	\(18\)	\(192\)	\(3\)	\(0\)	\(3\)
Plus space					\(+\)	\(3372\)	\(104\)	\(3268\)	\(3301\)	\(104\)	\(3197\)	\(71\)	\(0\)	\(71\)
Minus space					\(-\)	\(3420\)	\(124\)	\(3296\)	\(3348\)	\(124\)	\(3224\)	\(72\)	\(0\)	\(72\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(27300))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(27300))\) 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	27300.2.a
Level	$27300$
Weight	$2$
Character orbit	27300.a
Rep. character	$\chi_{27300}(1,\cdot)$
Character field	$\Q$
Dimension	$228$
Newform subspaces	$69$
Sturm bound	$13440$