Space of modular forms of level 2790, weight 2, and trivial character

• Label: 2790.2.a
• Level: $2790$
• Weight: $2$
• Character orbit: 2790.a
• Rep. character: $\chi_{2790}(1,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $37$
• Sturm bound: $1152$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 37 \)
Sturm bound:			\(1152\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2790))\).

	Total	New	Old
Modular forms	592	50	542
Cusp forms	561	50	511
Eisenstein series	31	0	31

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

\(2\)	\(3\)	\(5\)	\(31\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(5\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(5\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(5\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(1\)
Plus space				\(+\)	\(19\)
Minus space				\(-\)	\(31\)

Trace form

50 * q - 2 * q^2 + 50 * q^4 - 2 * q^5 - 2 * q^8 + 2 * q^10 - 8 * q^11 + 50 * q^16 + 4 * q^17 + 24 * q^19 - 2 * q^20 + 12 * q^22 + 8 * q^23 + 50 * q^25 + 4 * q^26 - 28 * q^29 - 2 * q^32 - 4 * q^34 - 8 * q^37 - 16 * q^38 + 2 * q^40 - 4 * q^41 + 20 * q^43 - 8 * q^44 + 16 * q^46 - 16 * q^47 + 50 * q^49 - 2 * q^50 + 24 * q^53 - 16 * q^55 - 16 * q^58 - 16 * q^59 + 12 * q^61 - 8 * q^62 + 50 * q^64 + 4 * q^65 + 16 * q^67 + 4 * q^68 + 16 * q^70 + 32 * q^71 + 28 * q^73 - 12 * q^74 + 24 * q^76 + 24 * q^77 + 16 * q^79 - 2 * q^80 - 12 * q^82 + 52 * q^83 + 24 * q^85 + 16 * q^86 + 12 * q^88 + 68 * q^89 + 72 * q^91 + 8 * q^92 - 8 * q^94 + 16 * q^95 + 12 * q^97 - 2 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2790))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	5	31
2790.2.a.a	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓			2790.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots\)
2790.2.a.b	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓			2790.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+2q^{11}+\cdots\)
2790.2.a.c	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.o	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+4q^{11}+\cdots\)
2790.2.a.d	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓			2790.2.a.d	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(-5\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-5q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.e	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				310.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.f	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.k	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.g	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓	✓	✓	2790.2.a.g	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.h	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				310.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
2790.2.a.i	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓			2790.2.a.i	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+4q^{11}+\cdots\)
2790.2.a.j	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.l	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+6q^{11}+\cdots\)
2790.2.a.k	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.n	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.l	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.m	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+3q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.m	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓			2790.2.a.m	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.n	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓			2790.2.a.d	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-5\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-5q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.o	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.c	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.p	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.h	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.q	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓	✓	✓	2790.2.a.g	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.r	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.i	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.s	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓			2790.2.a.i	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-4q^{11}+\cdots\)
2790.2.a.t	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.d	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.u	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.e	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.v	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.j	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.w	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓			2790.2.a.m	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.x	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓			2790.2.a.a	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-3\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots\)
2790.2.a.y	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓		✓	✓	930.2.a.a	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots\)
2790.2.a.z	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓	✓			2790.2.a.b	$1$	$1$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-2q^{11}+\cdots\)
2790.2.a.ba	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.b	$1$	$0$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots\)
2790.2.a.bb	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.f	$1$	$0$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
2790.2.a.bc	$2790$	$2$	2790.a	1.a	$1$	$1$	$1$	$22.278$	\(\Q\)	None	✓				930.2.a.g	$1$	$0$	\(1\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots\)
2790.2.a.bd	$2790$	$2$	2790.a	1.a	$1$	$2$	$2$	$22.278$	\(\Q(\sqrt{33}) \)	None	✓		✓		930.2.a.r	$1$	$0$	\(-2\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots\)
2790.2.a.be	$2790$	$2$	2790.a	1.a	$1$	$2$	$2$	$22.278$	\(\Q(\sqrt{17}) \)	None	✓				930.2.a.p	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+\beta q^{7}-q^{8}+q^{10}+\cdots\)
2790.2.a.bf	$2790$	$2$	2790.a	1.a	$1$	$2$	$2$	$22.278$	\(\Q(\sqrt{65}) \)	None	✓		✓		930.2.a.q	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-\beta q^{7}-q^{8}-q^{10}+\cdots\)
2790.2.a.bg	$2790$	$2$	2790.a	1.a	$1$	$2$	$2$	$22.278$	\(\Q(\sqrt{6}) \)	None	✓		✓		310.2.a.d	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
2790.2.a.bh	$2790$	$2$	2790.a	1.a	$1$	$2$	$2$	$22.278$	\(\Q(\sqrt{3}) \)	None	✓		✓		310.2.a.c	$1$	$0$	\(2\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+2\beta q^{7}+q^{8}+q^{10}+\cdots\)
2790.2.a.bi	$2790$	$2$	2790.a	1.a	$1$	$3$	$3$	$22.278$	3.3.148.1	None	✓		✓		310.2.a.e	$1$	$1$	\(-3\)	\(0\)	\(-3\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+(\beta _{1}-\beta _{2})q^{7}-q^{8}+\cdots\)
2790.2.a.bj	$2790$	$2$	2790.a	1.a	$1$	$4$	$4$	$22.278$	4.4.17428.1	None	✓	✓	✓	✓	2790.2.a.bj	$1$	$0$	\(-4\)	\(0\)	\(-4\)	\(5\)		$+$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+(1-\beta _{2})q^{7}-q^{8}+\cdots\)
2790.2.a.bk	$2790$	$2$	2790.a	1.a	$1$	$4$	$4$	$22.278$	4.4.17428.1	None	✓	✓	✓	✓	2790.2.a.bj	$1$	$0$	\(4\)	\(0\)	\(4\)	\(5\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+(1-\beta _{2})q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2790))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2790)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(279))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(558))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(930))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1395))\)\(^{\oplus 2}\)