Space of modular forms of level 2376, weight 2, and Character 2376.q

• Label: 2376.2.q
• Level: $2376$
• Weight: $2$
• Character orbit: 2376.q
• Rep. character: $\chi_{2376}(793,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $60$
• Newform subspaces: $8$
• Sturm bound: $864$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2376 = 2^{3} \cdot 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2376.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(864\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2376, [\chi])\).

	Total	New	Old
Modular forms	912	60	852
Cusp forms	816	60	756
Eisenstein series	96	0	96

Trace form

60 * q + 4 * q^5 - 6 * q^11 - 8 * q^23 - 30 * q^25 + 12 * q^29 + 12 * q^31 + 24 * q^35 - 4 * q^41 + 12 * q^43 - 6 * q^47 - 18 * q^49 - 36 * q^53 - 36 * q^59 + 12 * q^61 + 24 * q^65 + 8 * q^77 - 24 * q^85 - 48 * q^89 - 24 * q^91 + 32 * q^95 - 24 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(2376, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2376.2.q.a	$2376$	$2$	2376.q	9.c	$3$	$2$	$1$	$18.972$	\(\Q(\sqrt{-3}) \)	None					792.2.q.c	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-1+\zeta_{6})q^{11}+\cdots\)
2376.2.q.b	$2376$	$2$	2376.q	9.c	$3$	$2$	$1$	$18.972$	\(\Q(\sqrt{-3}) \)	None					792.2.q.b	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+(1-\zeta_{6})q^{11}+\cdots\)
2376.2.q.c	$2376$	$2$	2376.q	9.c	$3$	$2$	$1$	$18.972$	\(\Q(\sqrt{-3}) \)	None					792.2.q.a	$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{11}-2\zeta_{6}q^{13}+\cdots\)
2376.2.q.d	$2376$	$2$	2376.q	9.c	$3$	$4$	$2$	$18.972$	\(\Q(\zeta_{12})\)	None					792.2.q.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta_{2} q^{5}+(-\beta_{3}+\beta_{2}+\beta_1-1)q^{7}+\cdots\)
2376.2.q.e	$2376$	$2$	2376.q	9.c	$3$	$6$	$3$	$18.972$	6.0.309123.1	None					792.2.q.e	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2}+\beta _{4}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2376.2.q.f	$2376$	$2$	2376.q	9.c	$3$	$12$	$6$	$18.972$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					792.2.q.f	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-5\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{5}+\beta _{7})q^{5}+(-\beta _{1}-\beta _{5})q^{7}+\cdots\)
2376.2.q.g	$2376$	$2$	2376.q	9.c	$3$	$16$	$8$	$18.972$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					792.2.q.h	$2$	$0$	\(0\)	\(0\)	\(1\)	\(-5\)	$3^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{9}q^{5}+(-1+\beta _{8}-\beta _{14})q^{7}+(-1+\cdots)q^{11}+\cdots\)
2376.2.q.h	$2376$	$2$	2376.q	9.c	$3$	$16$	$8$	$18.972$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					792.2.q.g	$2$	$0$	\(0\)	\(0\)	\(3\)	\(5\)	$2^{2}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{5}-\beta _{15})q^{5}+(1+\beta _{1}+\beta _{2}-\beta _{9}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2376, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2376, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(297, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(594, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1188, [\chi])\)\(^{\oplus 2}\)