Space of modular forms of level 2790, weight 2, and Character 2790.d

• Label: 2790.2.d
• Level: $2790$
• Weight: $2$
• Character orbit: 2790.d
• Rep. character: $\chi_{2790}(559,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $15$
• Sturm bound: $1152$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2790.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(1152\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2790, [\chi])\).

	Total	New	Old
Modular forms	592	76	516
Cusp forms	560	76	484
Eisenstein series	32	0	32

Trace form

76 * q - 76 * q^4 - 4 * q^5 + 12 * q^11 + 8 * q^14 + 76 * q^16 + 16 * q^19 + 4 * q^20 - 12 * q^25 - 12 * q^26 - 4 * q^29 + 8 * q^34 - 8 * q^35 - 16 * q^41 - 12 * q^44 - 16 * q^46 - 92 * q^49 + 16 * q^50 + 36 * q^55 - 8 * q^56 - 32 * q^59 - 36 * q^61 - 76 * q^64 + 28 * q^65 - 32 * q^71 + 4 * q^74 - 16 * q^76 + 24 * q^79 - 4 * q^80 - 12 * q^85 + 20 * q^86 + 72 * q^89 - 64 * q^91 + 32 * q^94 + 24 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(2790, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2790.2.d.a	$2790$	$2$	2790.d	5.b	$2$	$2$	$2$	$22.278$	\(\Q(\sqrt{-1}) \)	None		✓			2790.2.d.a	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(i-2)q^{5}+2 i q^{7}+\cdots\)
2790.2.d.b	$2790$	$2$	2790.d	5.b	$2$	$2$	$2$	$22.278$	\(\Q(\sqrt{-1}) \)	None					930.2.d.f	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(i-2)q^{5}+2 i q^{7}+\cdots\)
2790.2.d.c	$2790$	$2$	2790.d	5.b	$2$	$2$	$2$	$22.278$	\(\Q(\sqrt{-1}) \)	None					930.2.d.e	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+(-i-2)q^{5}+2 i q^{7}+\cdots\)
2790.2.d.d	$2790$	$2$	2790.d	5.b	$2$	$2$	$2$	$22.278$	\(\Q(\sqrt{-1}) \)	None					930.2.d.d	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(-i-2)q^{5}+2 i q^{7}+\cdots\)
2790.2.d.e	$2790$	$2$	2790.d	5.b	$2$	$2$	$2$	$22.278$	\(\Q(\sqrt{-1}) \)	None					930.2.d.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(-2 i-1)q^{5}+5 i q^{7}+\cdots\)
2790.2.d.f	$2790$	$2$	2790.d	5.b	$2$	$2$	$2$	$22.278$	\(\Q(\sqrt{-1}) \)	None					930.2.d.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+(-2 i+1)q^{5}+i q^{7}+\cdots\)
2790.2.d.g	$2790$	$2$	2790.d	5.b	$2$	$2$	$2$	$22.278$	\(\Q(\sqrt{-1}) \)	None					930.2.d.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+(2 i+1)q^{5}+i q^{7}+\cdots\)
2790.2.d.h	$2790$	$2$	2790.d	5.b	$2$	$2$	$2$	$22.278$	\(\Q(\sqrt{-1}) \)	None		✓			2790.2.d.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+(-i+2)q^{5}+2 i q^{7}+\cdots\)
2790.2.d.i	$2790$	$2$	2790.d	5.b	$2$	$4$	$4$	$22.278$	\(\Q(\zeta_{8})\)	None					930.2.d.g	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}-q^{4}+(-\beta_1-2)q^{5}+\cdots\)
2790.2.d.j	$2790$	$2$	2790.d	5.b	$2$	$6$	$6$	$22.278$	6.0.11669056.1	None					930.2.d.i	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-q^{4}+(1-\beta _{1})q^{5}+2\beta _{3}q^{7}+\cdots\)
2790.2.d.k	$2790$	$2$	2790.d	5.b	$2$	$6$	$6$	$22.278$	6.0.3534400.1	None					930.2.d.h	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-q^{4}+(1-\beta _{4})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2790.2.d.l	$2790$	$2$	2790.d	5.b	$2$	$8$	$8$	$22.278$	8.0.2058981376.2	None					310.2.b.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-q^{4}+(1+\beta _{1}-\beta _{7})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2790.2.d.m	$2790$	$2$	2790.d	5.b	$2$	$8$	$8$	$22.278$	8.0.619810816.2	None					310.2.b.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+(\beta _{6}+\beta _{7})q^{5}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
2790.2.d.n	$2790$	$2$	2790.d	5.b	$2$	$12$	$12$	$22.278$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			2790.2.d.n	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(\beta _{6}+\beta _{7}+\beta _{11})q^{7}+\cdots\)
2790.2.d.o	$2790$	$2$	2790.d	5.b	$2$	$16$	$16$	$22.278$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		2790.2.d.o	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{2}-q^{4}+\beta _{6}q^{5}-\beta _{1}q^{7}-\beta _{9}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2790, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2790, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(930, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1395, [\chi])\)\(^{\oplus 2}\)