Space of modular forms of level 3312, weight 2, and Character 3312.e

• Label: 3312.2.e
• Level: $3312$
• Weight: $2$
• Character orbit: 3312.e
• Rep. character: $\chi_{3312}(1151,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $8$
• Sturm bound: $1152$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3312.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1152\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3312, [\chi])\).

	Total	New	Old
Modular forms	600	44	556
Cusp forms	552	44	508
Eisenstein series	48	0	48

Trace form

\( 44 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3312, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3312.2.e.a	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+2\beta q^{7}-4q^{11}-4q^{13}+3\beta q^{17}+\cdots\)
3312.2.e.b	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}-\beta q^{7}-2q^{11}+2q^{13}-5\beta q^{19}+\cdots\)
3312.2.e.c	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta q^{7}-2q^{11}+2q^{13}+2\beta q^{17}+\cdots\)
3312.2.e.d	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta q^{7}+2q^{11}+2q^{13}+2\beta q^{17}+\cdots\)
3312.2.e.e	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+\beta q^{7}+2q^{11}+2q^{13}+5\beta q^{19}+\cdots\)
3312.2.e.f	$3312$	$2$	3312.e	12.b	$2$	$2$	$2$	$26.446$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2\beta q^{7}+4q^{11}-4q^{13}+3\beta q^{17}+\cdots\)
3312.2.e.g	$3312$	$2$	3312.e	12.b	$2$	$16$	$16$	$26.446$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}-\beta _{8}q^{7}+\beta _{10}q^{11}+(-1+\cdots)q^{13}+\cdots\)
3312.2.e.h	$3312$	$2$	3312.e	12.b	$2$	$16$	$16$	$26.446$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+\beta _{8}q^{7}-\beta _{10}q^{11}+(-1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3312, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3312, [\chi]) \cong \)