Space of modular forms of level 3330, weight 2, and Character 3330.e

• Label: 3330.2.e
• Level: $3330$
• Weight: $2$
• Character orbit: 3330.e
• Rep. character: $\chi_{3330}(739,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $8$
• Sturm bound: $1368$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1368\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3330, [\chi])\).

	Total	New	Old
Modular forms	700	96	604
Cusp forms	668	96	572
Eisenstein series	32	0	32

Trace form

\( 96 q + 96 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3330, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3330.2.e.a	$3330$	$2$	3330.e	185.d	$2$	$2$	$2$	$26.590$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+(2-i)q^{5}+3iq^{7}-q^{8}+\cdots\)
3330.2.e.b	$3330$	$2$	3330.e	185.d	$2$	$2$	$2$	$26.590$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+(-2+i)q^{5}+3iq^{7}+\cdots\)
3330.2.e.c	$3330$	$2$	3330.e	185.d	$2$	$10$	$10$	$26.590$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(-10\)	\(0\)	\(-3\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{5}q^{5}-\beta _{2}q^{7}-q^{8}+\cdots\)
3330.2.e.d	$3330$	$2$	3330.e	185.d	$2$	$10$	$10$	$26.590$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(10\)	\(0\)	\(3\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{5}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots\)
3330.2.e.e	$3330$	$2$	3330.e	185.d	$2$	$16$	$16$	$26.590$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-16\)	\(0\)	\(-2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-\beta _{11}q^{5}-\beta _{14}q^{7}-q^{8}+\cdots\)
3330.2.e.f	$3330$	$2$	3330.e	185.d	$2$	$16$	$16$	$26.590$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(16\)	\(0\)	\(2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+\beta _{11}q^{5}-\beta _{14}q^{7}+q^{8}+\cdots\)
3330.2.e.g	$3330$	$2$	3330.e	185.d	$2$	$20$	$20$	$26.590$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(-20\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{10}q^{5}-\beta _{11}q^{7}-q^{8}+\cdots\)
3330.2.e.h	$3330$	$2$	3330.e	185.d	$2$	$20$	$20$	$26.590$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(20\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{10}q^{5}-\beta _{11}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3330, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \cong \)