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

• Label: 330.2.m
• Level: $330$
• Weight: $2$
• Character orbit: 330.m
• Rep. character: $\chi_{330}(31,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $32$
• Newform subspaces: $6$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.m (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	320	32	288
Cusp forms	256	32	224
Eisenstein series	64	0	64

Trace form

\( 32 q - 8 q^{4} - 8 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
330.2.m.a	$330$	$2$	330.m	11.c	$5$	$4$	$1$	$2.635$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-1\)	\(1\)	\(-1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
330.2.m.b	$330$	$2$	330.m	11.c	$5$	$4$	$1$	$2.635$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(-1\)	\(1\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
330.2.m.c	$330$	$2$	330.m	11.c	$5$	$4$	$1$	$2.635$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(1\)	\(1\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
330.2.m.d	$330$	$2$	330.m	11.c	$5$	$4$	$1$	$2.635$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(1\)	\(1\)	\(1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
330.2.m.e	$330$	$2$	330.m	11.c	$5$	$8$	$2$	$2.635$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{2}q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
330.2.m.f	$330$	$2$	330.m	11.c	$5$	$8$	$2$	$2.635$	8.0.2769390625.1	None		$2$	$0$	\(2\)	\(-2\)	\(2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{5}q^{2}+(-1-\beta _{2}+\beta _{3}-\beta _{5})q^{3}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)