Space of modular forms of level 335, weight 2, and Character 335.e

• Label: 335.2.e
• Level: $335$
• Weight: $2$
• Character orbit: 335.e
• Rep. character: $\chi_{335}(96,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $44$
• Newform subspaces: $2$
• Sturm bound: $68$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 335 = 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	335.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 67 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(68\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(335, [\chi])\).

	Total	New	Old
Modular forms	72	44	28
Cusp forms	64	44	20
Eisenstein series	8	0	8

Trace form

\( 44 q - 6 q^{2} - 24 q^{4} + 4 q^{5} + 4 q^{6} - 6 q^{7} + 36 q^{8} + 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(335, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
335.2.e.a	$335$	$2$	335.e	67.c	$3$	$20$	$10$	$2.675$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-3\)	\(0\)	\(-20\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(\beta _{10}-\beta _{18})q^{4}+\cdots\)
335.2.e.b	$335$	$2$	335.e	67.c	$3$	$24$	$12$	$2.675$		None		$2$	$0$	\(-3\)	\(0\)	\(24\)	\(-2\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(335, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(335, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 2}\)