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

• Label: 308.2.y
• Level: $308$
• Weight: $2$
• Character orbit: 308.y
• Rep. character: $\chi_{308}(9,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.y (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	432	64	368
Cusp forms	336	64	272
Eisenstein series	96	0	96

Trace form

\( 64 q + 2 q^{5} + 7 q^{7} + 14 q^{9} + O(q^{10}) \)

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.y.a	$308$	$2$	308.y	77.m	$15$	$16$	$2$	$2.459$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(1\)	\(-5\)	\(14\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-\beta _{3}+\beta _{6}+\beta _{7}+\beta _{12}-\beta _{15})q^{3}+\cdots\)
308.2.y.b	$308$	$2$	308.y	77.m	$15$	$48$	$6$	$2.459$		None		$4$	$0$	\(0\)	\(-1\)	\(7\)	\(-7\)		$\mathrm{SU}(2)[C_{15}]$

Decomposition of \(S_{2}^{\mathrm{old}}(308, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(308, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)