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

• Label: 308.2.n
• Level: $308$
• Weight: $2$
• Character orbit: 308.n
• Rep. character: $\chi_{308}(219,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 308 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(43\)

Dimensions

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

	Total	New	Old
Modular forms	104	104	0
Cusp forms	88	88	0
Eisenstein series	16	16	0

Trace form

\( 88 q - 4 q^{5} + 32 q^{9} + O(q^{10}) \)

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.n.a	$308$	$2$	308.n	308.n	$6$	$4$	$2$	$2.459$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(1-2\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
308.2.n.b	$308$	$2$	308.n	308.n	$6$	$4$	$2$	$2.459$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$4$	$0$	\(1\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(1-2\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
308.2.n.c	$308$	$2$	308.n	308.n	$6$	$80$	$40$	$2.459$		None		$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$