Space of modular forms of level 351, weight 2, and Character 351.t

• Label: 351.2.t
• Level: $351$
• Weight: $2$
• Character orbit: 351.t
• Rep. character: $\chi_{351}(64,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $84$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(84\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(351, [\chi])\).

	Total	New	Old
Modular forms	96	32	64
Cusp forms	72	24	48
Eisenstein series	24	8	16

Trace form

24 * q + 8 * q^4 - 16 * q^10 - 2 * q^13 + 18 * q^14 - 4 * q^16 + 24 * q^17 - 10 * q^22 - 18 * q^23 + 2 * q^25 + 12 * q^26 - 36 * q^35 - 12 * q^38 - 8 * q^40 + 6 * q^43 + 4 * q^52 - 72 * q^53 - 28 * q^55 - 36 * q^56 - 16 * q^61 + 72 * q^62 + 40 * q^64 - 36 * q^68 + 42 * q^74 + 30 * q^77 - 16 * q^79 - 4 * q^82 + 22 * q^88 - 24 * q^91 + 96 * q^92 + 20 * q^94 - 48 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(351, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
351.2.t.a	$351$	$2$	351.t	117.t	$6$	$2$	$1$	$2.803$	\(\Q(\sqrt{-3}) \)	None					117.2.t.a	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\zeta_{6})q^{4}+(-2-2\zeta_{6})q^{5}+\cdots\)
351.2.t.b	$351$	$2$	351.t	117.t	$6$	$2$	$1$	$2.803$	\(\Q(\sqrt{-3}) \)	None					117.2.t.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+2\zeta_{6})q^{4}+(2+2\zeta_{6})q^{5}+(-4+\cdots)q^{7}+\cdots\)
351.2.t.c	$351$	$2$	351.t	117.t	$6$	$20$	$10$	$2.803$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None			✓		117.2.t.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{9}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{15}q^{2}+(\beta _{5}+\beta _{8})q^{4}-\beta _{4}q^{5}+(\beta _{12}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(351, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(351, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)