Space of modular forms of level 308, weight 2, and Character 308.t

• Label: 308.2.t
• Level: $308$
• Weight: $2$
• Character orbit: 308.t
• Rep. character: $\chi_{308}(27,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $176$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.t (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 308 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(71\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(308, [\chi])\).

	Total	New	Old
Modular forms	208	208	0
Cusp forms	176	176	0
Eisenstein series	32	32	0

Trace form

\( 176 q - 8 q^{2} - 4 q^{4} - 8 q^{8} - 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(308, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
308.2.t.a	$308$	$2$	308.t	308.t	$10$	$8$	$2$	$2.459$	8.0.37515625.1	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
308.2.t.b	$308$	$2$	308.t	308.t	$10$	$8$	$2$	$2.459$	8.0.37515625.1	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
308.2.t.c	$308$	$2$	308.t	308.t	$10$	$160$	$40$	$2.459$		None		$8$	$0$	\(-10\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$