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

• Label: 330.2.l
• Level: $330$
• Weight: $2$
• Character orbit: 330.l
• Rep. character: $\chi_{330}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	160	24	136
Cusp forms	128	24	104
Eisenstein series	32	0	32

Trace form

24 * q - 16 * q^5 + 8 * q^11 + 8 * q^15 - 24 * q^16 - 4 * q^22 + 16 * q^23 + 16 * q^26 + 16 * q^31 - 12 * q^33 - 24 * q^36 + 32 * q^37 - 8 * q^42 - 32 * q^47 - 48 * q^53 + 36 * q^55 - 16 * q^56 - 8 * q^58 - 16 * q^60 - 8 * q^66 + 8 * q^70 + 16 * q^75 + 16 * q^80 - 24 * q^81 + 16 * q^82 + 32 * q^86 - 4 * q^88 - 16 * q^92 + 16 * q^93 - 24 * q^97

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.l.a	$330$	$2$	330.l	55.e	$4$	$4$	$2$	$2.635$	\(\Q(\zeta_{8})\)	None		✓			330.2.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
330.2.l.b	$330$	$2$	330.l	55.e	$4$	$4$	$2$	$2.635$	\(\Q(\zeta_{8})\)	None		✓			330.2.l.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots\)
330.2.l.c	$330$	$2$	330.l	55.e	$4$	$8$	$4$	$2.635$	8.0.822083584.4	None		✓			330.2.l.c	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}-\beta _{2}q^{3}+\beta _{4}q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots\)
330.2.l.d	$330$	$2$	330.l	55.e	$4$	$8$	$4$	$2.635$	8.0.822083584.4	None		✓			330.2.l.c	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{2}+\beta _{6}q^{3}-\beta _{4}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)

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

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