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

• Label: 2394.2.cq
• Level: $2394$
• Weight: $2$
• Character orbit: 2394.cq
• Rep. character: $\chi_{2394}(449,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $960$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.cq (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(960\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	992	80	912
Cusp forms	928	80	848
Eisenstein series	64	0	64

Trace form

80 * q - 40 * q^4 - 40 * q^16 - 16 * q^19 + 24 * q^22 + 32 * q^25 - 16 * q^43 + 80 * q^49 + 48 * q^55 + 32 * q^58 + 16 * q^61 + 80 * q^64 - 48 * q^67 + 24 * q^70 - 16 * q^73 - 16 * q^76 + 48 * q^79 + 32 * q^82 + 24 * q^85 + 96 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2394.2.cq.a	$2394$	$2$	2394.cq	57.f	$6$	$4$	$2$	$19.116$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			2394.2.cq.a	$2$	$0$	\(-2\)	\(0\)	\(6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(2+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
2394.2.cq.b	$2394$	$2$	2394.cq	57.f	$6$	$4$	$2$	$19.116$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			2394.2.cq.a	$2$	$0$	\(2\)	\(0\)	\(-6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
2394.2.cq.c	$2394$	$2$	2394.cq	57.f	$6$	$16$	$8$	$19.116$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			2394.2.cq.c	$2$	$0$	\(-8\)	\(0\)	\(-12\)	\(16\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{11})q^{2}-\beta _{11}q^{4}+(-1-\beta _{10}+\cdots)q^{5}+\cdots\)
2394.2.cq.d	$2394$	$2$	2394.cq	57.f	$6$	$16$	$8$	$19.116$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			2394.2.cq.c	$2$	$0$	\(8\)	\(0\)	\(12\)	\(16\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{11})q^{2}-\beta _{11}q^{4}+(1+\beta _{10}+\cdots)q^{5}+\cdots\)
2394.2.cq.e	$2394$	$2$	2394.cq	57.f	$6$	$20$	$10$	$19.116$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			2394.2.cq.e	$2$	$0$	\(-10\)	\(0\)	\(6\)	\(-20\)	$2^{2}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{7})q^{2}+\beta _{7}q^{4}-\beta _{2}q^{5}-q^{7}+\cdots\)
2394.2.cq.f	$2394$	$2$	2394.cq	57.f	$6$	$20$	$10$	$19.116$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			2394.2.cq.e	$2$	$0$	\(10\)	\(0\)	\(-6\)	\(-20\)	$2^{2}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{7})q^{2}+\beta _{7}q^{4}+\beta _{2}q^{5}-q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2394, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1197, [\chi])\)\(^{\oplus 2}\)