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

• Label: 308.2.z
• Level: $308$
• Weight: $2$
• Character orbit: 308.z
• Rep. character: $\chi_{308}(17,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $64$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	308.z (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

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 - 6 * q^5 + 5 * q^7 - 14 * q^9 + q^11 + 24 * q^15 - 30 * q^17 + 2 * q^23 - 14 * q^25 + 20 * q^29 - 18 * q^31 + 54 * q^33 - 45 * q^35 - 2 * q^37 + 20 * q^39 + 18 * q^45 + 12 * q^47 + 9 * q^49 - 28 * q^53 - 80 * q^57 + 30 * q^59 - 15 * q^61 + 35 * q^63 - 32 * q^67 - 44 * q^71 - 45 * q^73 - 126 * q^75 + 25 * q^77 - 15 * q^79 - 42 * q^81 - 130 * q^85 - 18 * q^89 - 26 * q^91 - 5 * q^93 + 35 * q^95 - 28 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
308.2.z.a	$308$	$2$	308.z	77.n	$30$	$64$	$8$	$2.459$		None		✓	✓	✓	308.2.z.a	$4$	$0$	\(0\)	\(0\)	\(-6\)	\(5\)		$\mathrm{SU}(2)[C_{30}]$

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

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