Space of modular forms of level 2394, weight 2, and Character 2394.e

• Label: 2394.2.e
• Level: $2394$
• Weight: $2$
• Character orbit: 2394.e
• Rep. character: $\chi_{2394}(1063,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $960$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(960\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2394, [\chi])\).

	Total	New	Old
Modular forms	496	64	432
Cusp forms	464	64	400
Eisenstein series	32	0	32

Trace form

\( 64 q - 64 q^{4} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2394, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2394.2.e.a	$2394$	$2$	2394.e	133.c	$2$	$12$	$12$	$19.116$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-q^{4}-\beta _{2}q^{5}+\beta _{7}q^{7}-\beta _{4}q^{8}+\cdots\)
2394.2.e.b	$2394$	$2$	2394.e	133.c	$2$	$12$	$12$	$19.116$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-q^{4}-\beta _{2}q^{5}+\beta _{7}q^{7}+\beta _{4}q^{8}+\cdots\)
2394.2.e.c	$2394$	$2$	2394.e	133.c	$2$	$16$	$16$	$19.116$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{2}-q^{4}-\beta _{7}q^{5}+\beta _{12}q^{7}+\cdots\)
2394.2.e.d	$2394$	$2$	2394.e	133.c	$2$	$24$	$24$	$19.116$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2394, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)