Space of modular forms of level 790, weight 2, and Character 790.m

• Label: 790.2.m
• Level: $790$
• Weight: $2$
• Character orbit: 790.m
• Rep. character: $\chi_{790}(21,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $288$
• Newform subspaces: $6$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 790 = 2 \cdot 5 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	790.m (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q(\zeta_{13})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(790, [\chi])\).

	Total	New	Old
Modular forms	1488	288	1200
Cusp forms	1392	288	1104
Eisenstein series	96	0	96

Trace form

288 * q + 4 * q^3 - 24 * q^4 + 16 * q^7 - 8 * q^9 + 16 * q^11 + 4 * q^12 + 24 * q^13 - 44 * q^15 - 24 * q^16 + 16 * q^17 + 16 * q^18 + 16 * q^19 - 20 * q^21 + 8 * q^23 - 24 * q^25 + 16 * q^26 + 40 * q^27 + 16 * q^28 + 32 * q^29 + 4 * q^30 + 32 * q^31 + 48 * q^33 + 24 * q^34 + 4 * q^35 - 8 * q^36 - 52 * q^37 + 8 * q^38 + 20 * q^39 + 16 * q^41 - 72 * q^42 + 36 * q^43 - 36 * q^44 + 16 * q^46 - 56 * q^47 + 4 * q^48 - 48 * q^49 + 32 * q^51 + 24 * q^52 + 60 * q^53 + 24 * q^54 + 24 * q^55 + 120 * q^57 + 36 * q^58 + 80 * q^59 + 8 * q^60 + 80 * q^61 + 40 * q^62 - 268 * q^63 - 24 * q^64 + 16 * q^65 - 12 * q^66 - 260 * q^67 - 36 * q^68 + 48 * q^69 + 4 * q^70 - 28 * q^71 + 16 * q^72 - 24 * q^73 - 36 * q^74 + 4 * q^75 - 88 * q^76 - 304 * q^77 - 40 * q^78 - 76 * q^79 - 36 * q^81 - 48 * q^82 - 44 * q^83 - 20 * q^84 + 28 * q^85 + 20 * q^86 - 260 * q^87 + 44 * q^89 + 56 * q^91 - 44 * q^92 - 204 * q^93 + 4 * q^94 + 24 * q^95 - 152 * q^97 - 72 * q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(790, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
790.2.m.a	$790$	$2$	790.m	79.e	$13$	$12$	$1$	$6.308$	\(\Q(\zeta_{26})\)	None		✓			790.2.m.a	$2$	$0$	\(1\)	\(-9\)	\(-1\)	\(17\)	$1$	$\mathrm{SU}(2)[C_{13}]$	\(q+\zeta_{26}q^{2}+(-1-\zeta_{26}^{2}+\zeta_{26}^{5}+\zeta_{26}^{7}+\cdots)q^{3}+\cdots\)
790.2.m.b	$790$	$2$	790.m	79.e	$13$	$12$	$1$	$6.308$	\(\Q(\zeta_{26})\)	None		✓			790.2.m.b	$2$	$0$	\(1\)	\(12\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{13}]$	\(q+\zeta_{26}q^{2}+(1-\zeta_{26}^{7}-\zeta_{26}^{10})q^{3}+\cdots\)
790.2.m.c	$790$	$2$	790.m	79.e	$13$	$48$	$4$	$6.308$		None		✓			790.2.m.c	$2$	$0$	\(4\)	\(-1\)	\(-4\)	\(-9\)		$\mathrm{SU}(2)[C_{13}]$
790.2.m.d	$790$	$2$	790.m	79.e	$13$	$72$	$6$	$6.308$		None		✓			790.2.m.d	$2$	$0$	\(-6\)	\(-2\)	\(6\)	\(2\)		$\mathrm{SU}(2)[C_{13}]$
790.2.m.e	$790$	$2$	790.m	79.e	$13$	$72$	$6$	$6.308$		None		✓			790.2.m.e	$2$	$0$	\(-6\)	\(4\)	\(-6\)	\(6\)		$\mathrm{SU}(2)[C_{13}]$
790.2.m.f	$790$	$2$	790.m	79.e	$13$	$72$	$6$	$6.308$		None		✓			790.2.m.f	$2$	$0$	\(6\)	\(0\)	\(6\)	\(4\)		$\mathrm{SU}(2)[C_{13}]$

Decomposition of \(S_{2}^{\mathrm{old}}(790, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(790, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(158, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(395, [\chi])\)\(^{\oplus 2}\)