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

• Label: 330.2.j
• Level: $330$
• Weight: $2$
• Character orbit: 330.j
• Rep. character: $\chi_{330}(23,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(17\)

Dimensions

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

	Total	New	Old
Modular forms	160	40	120
Cusp forms	128	40	88
Eisenstein series	32	0	32

Trace form

\( 40 q + 4 q^{3} + 8 q^{6} + O(q^{10}) \)

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.j.a	$330$	$2$	330.j	15.e	$4$	$20$	$10$	$2.635$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{2}-\beta _{3}q^{3}-\beta _{14}q^{4}+(\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
330.2.j.b	$330$	$2$	330.j	15.e	$4$	$20$	$10$	$2.635$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}+\beta _{1}q^{3}-\beta _{14}q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)