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

• Label: 3312.2.i
• Level: $3312$
• Weight: $2$
• Character orbit: 3312.i
• Rep. character: $\chi_{3312}(2575,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $7$
• Sturm bound: $1152$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3312.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 92 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1152\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	600	60	540
Cusp forms	552	60	492
Eisenstein series	48	0	48

Trace form

\( 60 q + O(q^{10}) \)

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.i.a	$3312$	$2$	3312.i	92.b	$2$	$4$	$4$	$26.446$	\(\Q(\sqrt{2}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+\beta _{1}q^{7}-3\beta _{1}q^{11}+3q^{13}+\cdots\)
3312.2.i.b	$3312$	$2$	3312.i	92.b	$2$	$8$	$8$	$26.446$	8.0.56070144.2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+\beta _{4}q^{7}+(-3+\beta _{5})q^{11}+\cdots\)
3312.2.i.c	$3312$	$2$	3312.i	92.b	$2$	$8$	$8$	$26.446$	8.0.\(\cdots\).8	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}-\beta _{4}q^{7}+2\beta _{1}q^{11}+(-2+\cdots)q^{13}+\cdots\)
3312.2.i.d	$3312$	$2$	3312.i	92.b	$2$	$8$	$8$	$26.446$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}+(-\beta _{3}+\beta _{6})q^{7}+\beta _{3}q^{11}+\cdots\)
3312.2.i.e	$3312$	$2$	3312.i	92.b	$2$	$8$	$8$	$26.446$	8.0.\(\cdots\).105	\(\Q(\sqrt{-69}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{4}q^{5}-\beta _{3}q^{7}-\beta _{1}q^{13}+(\beta _{4}+\beta _{7})q^{17}+\cdots\)
3312.2.i.f	$3312$	$2$	3312.i	92.b	$2$	$8$	$8$	$26.446$	8.0.56070144.2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+\beta _{4}q^{7}+(3-\beta _{5})q^{11}+2\beta _{5}q^{13}+\cdots\)
3312.2.i.g	$3312$	$2$	3312.i	92.b	$2$	$16$	$16$	$26.446$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{12}q^{5}-\beta _{8}q^{7}-\beta _{6}q^{11}+(1-\beta _{1}+\cdots)q^{13}+\cdots\)

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

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