LMFDB - Space of modular forms of level 29640, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 29640 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	29640.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 60 $
Sturm bound:			$13440$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(29640))$.

	Total	New	Old
Modular forms	6752	432	6320
Cusp forms	6689	432	6257
Eisenstein series	63	0	63

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

$2$	$3$	$5$	$13$	$19$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$13$	$19$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$+$	$200$	$13$	$187$	$199$	$13$	$186$	$1$	$0$	$1$
$+$	$+$	$+$	$+$	$-$	$-$	$220$	$12$	$208$	$218$	$12$	$206$	$2$	$0$	$2$
$+$	$+$	$+$	$-$	$+$	$-$	$212$	$14$	$198$	$210$	$14$	$196$	$2$	$0$	$2$
$+$	$+$	$+$	$-$	$-$	$+$	$212$	$15$	$197$	$210$	$15$	$195$	$2$	$0$	$2$
$+$	$+$	$-$	$+$	$+$	$-$	$213$	$15$	$198$	$211$	$15$	$196$	$2$	$0$	$2$
$+$	$+$	$-$	$+$	$-$	$+$	$211$	$14$	$197$	$209$	$14$	$195$	$2$	$0$	$2$
$+$	$+$	$-$	$-$	$+$	$+$	$215$	$11$	$204$	$213$	$11$	$202$	$2$	$0$	$2$
$+$	$+$	$-$	$-$	$-$	$-$	$205$	$14$	$191$	$203$	$14$	$189$	$2$	$0$	$2$
$+$	$-$	$+$	$+$	$+$	$-$	$207$	$15$	$192$	$205$	$15$	$190$	$2$	$0$	$2$
$+$	$-$	$+$	$+$	$-$	$+$	$217$	$13$	$204$	$215$	$13$	$202$	$2$	$0$	$2$
$+$	$-$	$+$	$-$	$+$	$+$	$209$	$11$	$198$	$207$	$11$	$196$	$2$	$0$	$2$
$+$	$-$	$+$	$-$	$-$	$-$	$211$	$15$	$196$	$209$	$15$	$194$	$2$	$0$	$2$
$+$	$-$	$-$	$+$	$+$	$+$	$210$	$11$	$199$	$208$	$11$	$197$	$2$	$0$	$2$
$+$	$-$	$-$	$+$	$-$	$-$	$210$	$15$	$195$	$208$	$15$	$193$	$2$	$0$	$2$
$+$	$-$	$-$	$-$	$+$	$-$	$222$	$18$	$204$	$220$	$18$	$202$	$2$	$0$	$2$
$+$	$-$	$-$	$-$	$-$	$+$	$202$	$10$	$192$	$200$	$10$	$190$	$2$	$0$	$2$
$-$	$+$	$+$	$+$	$+$	$-$	$214$	$11$	$203$	$212$	$11$	$201$	$2$	$0$	$2$
$-$	$+$	$+$	$+$	$-$	$+$	$210$	$15$	$195$	$208$	$15$	$193$	$2$	$0$	$2$
$-$	$+$	$+$	$-$	$+$	$+$	$202$	$15$	$187$	$200$	$15$	$185$	$2$	$0$	$2$
$-$	$+$	$+$	$-$	$-$	$-$	$218$	$13$	$205$	$216$	$13$	$203$	$2$	$0$	$2$
$-$	$+$	$-$	$+$	$+$	$+$	$217$	$14$	$203$	$215$	$14$	$201$	$2$	$0$	$2$
$-$	$+$	$-$	$+$	$-$	$-$	$203$	$14$	$189$	$201$	$14$	$187$	$2$	$0$	$2$
$-$	$+$	$-$	$-$	$+$	$-$	$215$	$13$	$202$	$213$	$13$	$200$	$2$	$0$	$2$
$-$	$+$	$-$	$-$	$-$	$+$	$209$	$13$	$196$	$207$	$13$	$194$	$2$	$0$	$2$
$-$	$-$	$+$	$+$	$+$	$+$	$207$	$15$	$192$	$205$	$15$	$190$	$2$	$0$	$2$
$-$	$-$	$+$	$+$	$-$	$-$	$213$	$14$	$199$	$211$	$14$	$197$	$2$	$0$	$2$
$-$	$-$	$+$	$-$	$+$	$-$	$205$	$14$	$191$	$203$	$14$	$189$	$2$	$0$	$2$
$-$	$-$	$+$	$-$	$-$	$+$	$219$	$11$	$208$	$217$	$11$	$206$	$2$	$0$	$2$
$-$	$-$	$-$	$+$	$+$	$-$	$220$	$14$	$206$	$218$	$14$	$204$	$2$	$0$	$2$
$-$	$-$	$-$	$+$	$-$	$+$	$204$	$11$	$193$	$202$	$11$	$191$	$2$	$0$	$2$
$-$	$-$	$-$	$-$	$+$	$+$	$208$	$12$	$196$	$206$	$12$	$194$	$2$	$0$	$2$
$-$	$-$	$-$	$-$	$-$	$-$	$212$	$17$	$195$	$210$	$17$	$193$	$2$	$0$	$2$
Plus space					$+$	$3352$	$204$	$3148$	$3321$	$204$	$3117$	$31$	$0$	$31$
Minus space					$-$	$3400$	$228$	$3172$	$3368$	$228$	$3140$	$32$	$0$	$32$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(29640))$ 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	13	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
29640.2.a.a	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.a	$1$		$0$	$-1$	$-1$	$-4$	$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}+q^{9}-6q^{11}+q^{13}+\cdots$
29640.2.a.b	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.b	$1$		$0$	$-1$	$-1$	$-4$	$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}+q^{9}-2q^{11}-q^{13}+\cdots$
29640.2.a.c	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.c	$1$		$0$	$-1$	$-1$	$-2$	$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}-q^{13}+\cdots$
29640.2.a.d	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.d	$1$		$0$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}-3q^{11}+q^{13}+\cdots$
29640.2.a.e	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.e	$1$		$0$	$-1$	$-1$	$4$	$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}-q^{13}+\cdots$
29640.2.a.f	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.f	$1$		$0$	$-1$	$-1$	$5$	$-$	$+$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+5q^{7}+q^{9}+3q^{11}-q^{13}+\cdots$
29640.2.a.g	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.g	$1$		$0$	$-1$	$1$	$-4$	$+$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}-q^{13}+\cdots$
29640.2.a.h	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.h	$1$		$0$	$-1$	$1$	$-4$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}+q^{13}+\cdots$
29640.2.a.i	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.i	$1$		$0$	$-1$	$1$	$0$	$+$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-6q^{11}-q^{13}-q^{15}+\cdots$
29640.2.a.j	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.j	$1$		$0$	$-1$	$1$	$2$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}-6q^{11}+q^{13}+\cdots$
29640.2.a.k	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.k	$1$		$0$	$-1$	$1$	$2$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}+q^{13}-q^{15}+\cdots$
29640.2.a.l	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.l	$1$		$0$	$1$	$-1$	$-4$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}-q^{13}+\cdots$
29640.2.a.m	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.m	$1$		$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-4q^{11}-q^{13}-q^{15}+\cdots$
29640.2.a.n	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.n	$1$		$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+q^{13}-q^{15}-2q^{17}+\cdots$
29640.2.a.o	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.o	$1$		$0$	$1$	$-1$	$2$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}-q^{13}+\cdots$
29640.2.a.p	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.p	$1$		$0$	$1$	$1$	$-5$	$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-5q^{7}+q^{9}-5q^{11}+q^{13}+\cdots$
29640.2.a.q	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.q	$1$		$0$	$1$	$1$	$-4$	$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}-q^{13}+\cdots$
29640.2.a.r	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.r	$1$		$0$	$1$	$1$	$-4$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}+q^{13}+\cdots$
29640.2.a.s	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.s	$1$		$0$	$1$	$1$	$-2$	$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}-q^{13}+\cdots$
29640.2.a.t	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.t	$1$		$0$	$1$	$1$	$-2$	$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}-q^{13}+\cdots$
29640.2.a.u	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.u	$1$		$0$	$1$	$1$	$0$	$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-4q^{11}-q^{13}+q^{15}+\cdots$
29640.2.a.v	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.v	$1$		$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+4q^{11}+q^{13}+q^{15}+\cdots$
29640.2.a.w	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.w	$1$		$0$	$1$	$1$	$4$	$+$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}+q^{9}-5q^{11}+q^{13}+\cdots$
29640.2.a.x	$29640$	$2$	29640.a	1.a	$1$	$1$	$1$	$236.677$	$\Q$	None	✓	✓			29640.2.a.x	$1$		$0$	$1$	$1$	$4$	$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}+q^{9}+3q^{11}-q^{13}+\cdots$
29640.2.a.y	$29640$	$2$	29640.a	1.a	$1$	$2$	$2$	$236.677$	$\Q(\sqrt{17}) $	None	✓	✓			29640.2.a.y	$1$		$0$	$-2$	$-2$	$0$	$-$	$+$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
29640.2.a.z	$29640$	$2$	29640.a	1.a	$1$	$2$	$2$	$236.677$	$\Q(\sqrt{5}) $	None	✓	✓			29640.2.a.z	$1$		$0$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
29640.2.a.ba	$29640$	$2$	29640.a	1.a	$1$	$2$	$2$	$236.677$	$\Q(\sqrt{17}) $	None	✓	✓			29640.2.a.ba	$1$		$0$	$2$	$-2$	$0$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
29640.2.a.bb	$29640$	$2$	29640.a	1.a	$1$	$3$	$3$	$236.677$	3.3.568.1	None	✓	✓			29640.2.a.bb	$1$		$0$	$3$	$3$	$0$	$+$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
29640.2.a.bc	$29640$	$2$	29640.a	1.a	$1$	$9$	$9$	$236.677$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		29640.2.a.bc	$1$		$0$	$9$	$9$	$3$	$+$	$-$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
29640.2.a.bd	$29640$	$2$	29640.a	1.a	$1$	$9$	$9$	$236.677$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		29640.2.a.bd	$1$		$0$	$9$	$9$	$4$	$+$	$-$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
29640.2.a.be	$29640$	$2$	29640.a	1.a	$1$	$10$	$10$	$236.677$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		29640.2.a.be	$1$		$0$	$-10$	$-10$	$10$	$+$	$+$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
29640.2.a.bf	$29640$	$2$	29640.a	1.a	$1$	$10$	$10$	$236.677$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		29640.2.a.bf	$1$		$0$	$10$	$-10$	$-3$	$-$	$-$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
29640.2.a.bg	$29640$	$2$	29640.a	1.a	$1$	$10$	$10$	$236.677$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.bg	$1$		$0$	$10$	$10$	$-3$	$+$	$-$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
29640.2.a.bh	$29640$	$2$	29640.a	1.a	$1$	$11$	$11$	$236.677$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.bh	$1$		$0$	$-11$	$-11$	$-2$	$-$	$+$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
29640.2.a.bi	$29640$	$2$	29640.a	1.a	$1$	$11$	$11$	$236.677$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓		29640.2.a.bi	$1$		$0$	$-11$	$11$	$-8$	$-$	$+$	$-$	$-$	$-$	$+$		$\mathrm{SU}(2)$
29640.2.a.bj	$29640$	$2$	29640.a	1.a	$1$	$11$	$11$	$236.677$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.bj	$1$		$0$	$-11$	$11$	$4$	$+$	$+$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
29640.2.a.bk	$29640$	$2$	29640.a	1.a	$1$	$11$	$11$	$236.677$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.bk	$1$		$0$	$11$	$-11$	$-3$	$+$	$-$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
29640.2.a.bl	$29640$	$2$	29640.a	1.a	$1$	$11$	$11$	$236.677$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓		29640.2.a.bl	$1$		$0$	$11$	$-11$	$2$	$-$	$-$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
29640.2.a.bm	$29640$	$2$	29640.a	1.a	$1$	$11$	$11$	$236.677$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓		29640.2.a.bm	$1$		$0$	$11$	$11$	$-5$	$-$	$-$	$-$	$-$	$+$	$+$		$\mathrm{SU}(2)$
29640.2.a.bn	$29640$	$2$	29640.a	1.a	$1$	$11$	$11$	$236.677$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.bn	$1$		$0$	$11$	$11$	$-4$	$-$	$-$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
29640.2.a.bo	$29640$	$2$	29640.a	1.a	$1$	$12$	$12$	$236.677$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		29640.2.a.bo	$1$		$0$	$-12$	$-12$	$6$	$+$	$+$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
29640.2.a.bp	$29640$	$2$	29640.a	1.a	$1$	$12$	$12$	$236.677$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		29640.2.a.bp	$1$		$0$	$-12$	$12$	$7$	$+$	$+$	$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
29640.2.a.bq	$29640$	$2$	29640.a	1.a	$1$	$12$	$12$	$236.677$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		29640.2.a.bq	$1$		$0$	$-12$	$12$	$11$	$-$	$+$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
29640.2.a.br	$29640$	$2$	29640.a	1.a	$1$	$12$	$12$	$236.677$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		29640.2.a.br	$1$		$0$	$12$	$-12$	$0$	$-$	$-$	$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
29640.2.a.bs	$29640$	$2$	29640.a	1.a	$1$	$13$	$13$	$236.677$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.bs	$1$		$0$	$-13$	$-13$	$-7$	$+$	$+$	$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
29640.2.a.bt	$29640$	$2$	29640.a	1.a	$1$	$13$	$13$	$236.677$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓		29640.2.a.bt	$1$		$0$	$-13$	$-13$	$-4$	$-$	$+$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
29640.2.a.bu	$29640$	$2$	29640.a	1.a	$1$	$13$	$13$	$236.677$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.bu	$1$		$0$	$-13$	$-13$	$-3$	$-$	$+$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
29640.2.a.bv	$29640$	$2$	29640.a	1.a	$1$	$13$	$13$	$236.677$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓		29640.2.a.bv	$1$		$0$	$-13$	$-13$	$2$	$-$	$+$	$+$	$-$	$+$	$+$		$\mathrm{SU}(2)$
29640.2.a.bw	$29640$	$2$	29640.a	1.a	$1$	$13$	$13$	$236.677$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.bw	$1$		$0$	$13$	$-13$	$-10$	$+$	$-$	$+$	$+$	$-$	$+$		$\mathrm{SU}(2)$
29640.2.a.bx	$29640$	$2$	29640.a	1.a	$1$	$13$	$13$	$236.677$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	✓	✓		29640.2.a.bx	$1$		$0$	$13$	$-13$	$1$	$-$	$-$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
29640.2.a.by	$29640$	$2$	29640.a	1.a	$1$	$14$	$14$	$236.677$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.by	$1$		$0$	$-14$	$14$	$-3$	$-$	$+$	$-$	$+$	$+$	$+$		$\mathrm{SU}(2)$
29640.2.a.bz	$29640$	$2$	29640.a	1.a	$1$	$14$	$14$	$236.677$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.bz	$1$		$0$	$-14$	$14$	$-3$	$+$	$+$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
29640.2.a.ca	$29640$	$2$	29640.a	1.a	$1$	$14$	$14$	$236.677$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.ca	$1$		$0$	$-14$	$14$	$-2$	$-$	$+$	$-$	$+$	$-$	$-$		$\mathrm{SU}(2)$
29640.2.a.cb	$29640$	$2$	29640.a	1.a	$1$	$14$	$14$	$236.677$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.cb	$1$		$0$	$14$	$14$	$5$	$-$	$-$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
29640.2.a.cc	$29640$	$2$	29640.a	1.a	$1$	$15$	$15$	$236.677$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.cc	$1$		$0$	$-15$	$-15$	$0$	$+$	$+$	$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
29640.2.a.cd	$29640$	$2$	29640.a	1.a	$1$	$15$	$15$	$236.677$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.cd	$1$		$0$	$-15$	$15$	$-2$	$+$	$+$	$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$
29640.2.a.ce	$29640$	$2$	29640.a	1.a	$1$	$15$	$15$	$236.677$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.ce	$1$		$0$	$15$	$-15$	$6$	$+$	$-$	$+$	$-$	$-$	$-$		$\mathrm{SU}(2)$
29640.2.a.cf	$29640$	$2$	29640.a	1.a	$1$	$15$	$15$	$236.677$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	✓	✓	✓	29640.2.a.cf	$1$		$0$	$15$	$-15$	$9$	$+$	$-$	$+$	$+$	$+$	$-$		$\mathrm{SU}(2)$
29640.2.a.cg	$29640$	$2$	29640.a	1.a	$1$	$16$	$16$	$236.677$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	✓	✓		29640.2.a.cg	$1$		$0$	$16$	$16$	$-1$	$+$	$-$	$-$	$-$	$+$	$-$		$\mathrm{SU}(2)$
29640.2.a.ch	$29640$	$2$	29640.a	1.a	$1$	$16$	$16$	$236.677$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	✓	✓		29640.2.a.ch	$1$		$0$	$16$	$16$	$10$	$-$	$-$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(29640))$ 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:	\( N \)	\(=\)	\( 29640 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	29640.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 60 \)
Sturm bound:			\(13440\)

\(2\)	\(3\)	\(5\)	\(13\)	\(19\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(13\)	\(19\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(200\)	\(13\)	\(187\)	\(199\)	\(13\)	\(186\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(220\)	\(12\)	\(208\)	\(218\)	\(12\)	\(206\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(212\)	\(14\)	\(198\)	\(210\)	\(14\)	\(196\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(212\)	\(15\)	\(197\)	\(210\)	\(15\)	\(195\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(213\)	\(15\)	\(198\)	\(211\)	\(15\)	\(196\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(211\)	\(14\)	\(197\)	\(209\)	\(14\)	\(195\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(215\)	\(11\)	\(204\)	\(213\)	\(11\)	\(202\)	\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(205\)	\(14\)	\(191\)	\(203\)	\(14\)	\(189\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(207\)	\(15\)	\(192\)	\(205\)	\(15\)	\(190\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(217\)	\(13\)	\(204\)	\(215\)	\(13\)	\(202\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(209\)	\(11\)	\(198\)	\(207\)	\(11\)	\(196\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(211\)	\(15\)	\(196\)	\(209\)	\(15\)	\(194\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(210\)	\(11\)	\(199\)	\(208\)	\(11\)	\(197\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(210\)	\(15\)	\(195\)	\(208\)	\(15\)	\(193\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(222\)	\(18\)	\(204\)	\(220\)	\(18\)	\(202\)	\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(202\)	\(10\)	\(192\)	\(200\)	\(10\)	\(190\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(214\)	\(11\)	\(203\)	\(212\)	\(11\)	\(201\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(210\)	\(15\)	\(195\)	\(208\)	\(15\)	\(193\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(202\)	\(15\)	\(187\)	\(200\)	\(15\)	\(185\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(218\)	\(13\)	\(205\)	\(216\)	\(13\)	\(203\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(217\)	\(14\)	\(203\)	\(215\)	\(14\)	\(201\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(203\)	\(14\)	\(189\)	\(201\)	\(14\)	\(187\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(215\)	\(13\)	\(202\)	\(213\)	\(13\)	\(200\)	\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(209\)	\(13\)	\(196\)	\(207\)	\(13\)	\(194\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(207\)	\(15\)	\(192\)	\(205\)	\(15\)	\(190\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(213\)	\(14\)	\(199\)	\(211\)	\(14\)	\(197\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(205\)	\(14\)	\(191\)	\(203\)	\(14\)	\(189\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(219\)	\(11\)	\(208\)	\(217\)	\(11\)	\(206\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(220\)	\(14\)	\(206\)	\(218\)	\(14\)	\(204\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(204\)	\(11\)	\(193\)	\(202\)	\(11\)	\(191\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(208\)	\(12\)	\(196\)	\(206\)	\(12\)	\(194\)	\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(212\)	\(17\)	\(195\)	\(210\)	\(17\)	\(193\)	\(2\)	\(0\)	\(2\)
Plus space					\(+\)	\(3352\)	\(204\)	\(3148\)	\(3321\)	\(204\)	\(3117\)	\(31\)	\(0\)	\(31\)
Minus space					\(-\)	\(3400\)	\(228\)	\(3172\)	\(3368\)	\(228\)	\(3140\)	\(32\)	\(0\)	\(32\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(29640))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(29640))\) 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	29640.2.a
Level	$29640$
Weight	$2$
Character orbit	29640.a
Rep. character	$\chi_{29640}(1,\cdot)$
Character field	$\Q$
Dimension	$432$
Newform subspaces	$60$
Sturm bound	$13440$