Space of modular forms of level 330, weight 2, and Character 330.c

• Label: 330.2.c
• Level: $330$
• Weight: $2$
• Character orbit: 330.c
• Rep. character: $\chi_{330}(199,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(330, [\chi])\).

	Total	New	Old
Modular forms	80	8	72
Cusp forms	64	8	56
Eisenstein series	16	0	16

Trace form

8 * q - 8 * q^4 - 8 * q^9 + 8 * q^16 - 16 * q^19 + 16 * q^21 - 16 * q^25 + 16 * q^26 + 32 * q^31 - 32 * q^35 + 8 * q^36 - 16 * q^39 + 32 * q^41 - 24 * q^49 - 32 * q^50 + 48 * q^61 - 8 * q^64 - 32 * q^65 - 8 * q^66 + 16 * q^69 - 24 * q^70 + 48 * q^71 - 8 * q^75 + 16 * q^76 + 16 * q^79 + 8 * q^81 - 16 * q^84 - 48 * q^85 + 16 * q^86 - 16 * q^89 - 16 * q^91 + 32 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(330, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
330.2.c.a	$330$	$2$	330.c	5.b	$2$	$4$	$4$	$2.635$	\(\Q(i, \sqrt{10})\)	None		✓			330.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+\beta _{1}q^{5}-q^{6}+\cdots\)
330.2.c.b	$330$	$2$	330.c	5.b	$2$	$4$	$4$	$2.635$	\(\Q(\zeta_{8})\)	None		✓			330.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(330, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(330, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)