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

• Label: 2394.2.b
• Level: $2394$
• Weight: $2$
• Character orbit: 2394.b
• Rep. character: $\chi_{2394}(1709,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $10$
• Sturm bound: $960$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(960\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(29\), \(53\)

Dimensions

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

	Total	New	Old
Modular forms	496	40	456
Cusp forms	464	40	424
Eisenstein series	32	0	32

Trace form

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

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.b.a	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-q^{7}-q^{8}-\beta q^{13}+q^{14}+\cdots\)
2394.2.b.b	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+2\beta q^{5}+q^{7}-q^{8}-2\beta q^{10}+\cdots\)
2394.2.b.c	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
2394.2.b.d	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-\beta q^{13}-q^{14}+\cdots\)
2394.2.b.e	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+2\beta q^{5}+q^{7}+q^{8}+2\beta q^{10}+\cdots\)
2394.2.b.f	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
2394.2.b.g	$2394$	$2$	2394.b	57.d	$2$	$6$	$6$	$19.116$	6.0.2803712.1	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(6\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}-q^{8}+\beta _{1}q^{10}+\cdots\)
2394.2.b.h	$2394$	$2$	2394.b	57.d	$2$	$6$	$6$	$19.116$	6.0.2803712.1	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(6\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}+q^{8}-\beta _{1}q^{10}+\cdots\)
2394.2.b.i	$2394$	$2$	2394.b	57.d	$2$	$8$	$8$	$19.116$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(-8\)	\(0\)	\(0\)	\(-8\)	$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta _{3}q^{5}-q^{7}-q^{8}-\beta _{3}q^{10}+\cdots\)
2394.2.b.j	$2394$	$2$	2394.b	57.d	$2$	$8$	$8$	$19.116$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(8\)	\(0\)	\(0\)	\(-8\)	$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+\beta _{3}q^{5}-q^{7}+q^{8}+\beta _{3}q^{10}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \cong \)