Space of modular forms of level 2368, weight 2, and Character 2368.g

• Label: 2368.2.g
• Level: $2368$
• Weight: $2$
• Character orbit: 2368.g
• Rep. character: $\chi_{2368}(961,\cdot)$
• Character field: $\Q$
• Dimension: $74$
• Newform subspaces: $16$
• Sturm bound: $608$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2368 = 2^{6} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2368.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(608\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2368, [\chi])\).

	Total	New	Old
Modular forms	316	78	238
Cusp forms	292	74	218
Eisenstein series	24	4	20

Trace form

\( 74 q + 66 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2368, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2368.2.g.a	$2368$	$2$	2368.g	37.b	$2$	$2$	$2$	$18.909$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+3q^{7}+6q^{9}+3q^{11}+3iq^{13}+\cdots\)
2368.2.g.b	$2368$	$2$	2368.g	37.b	$2$	$2$	$2$	$18.909$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(0\)	\(-6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-iq^{5}-3q^{7}-2q^{9}-3q^{11}+\cdots\)
2368.2.g.c	$2368$	$2$	2368.g	37.b	$2$	$2$	$2$	$18.909$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\zeta_{6}q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots\)
2368.2.g.d	$2368$	$2$	2368.g	37.b	$2$	$2$	$2$	$18.909$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2iq^{5}-3q^{9}-2iq^{13}-4iq^{17}+\cdots\)
2368.2.g.e	$2368$	$2$	2368.g	37.b	$2$	$2$	$2$	$18.909$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\zeta_{6}q^{5}-q^{7}-2q^{9}+3q^{11}+\cdots\)
2368.2.g.f	$2368$	$2$	2368.g	37.b	$2$	$2$	$2$	$18.909$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-iq^{5}+3q^{7}-2q^{9}+3q^{11}+\cdots\)
2368.2.g.g	$2368$	$2$	2368.g	37.b	$2$	$2$	$2$	$18.909$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(-6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}-3q^{7}+6q^{9}-3q^{11}+3iq^{13}+\cdots\)
2368.2.g.h	$2368$	$2$	2368.g	37.b	$2$	$4$	$4$	$18.909$	\(\Q(i, \sqrt{21})\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(8\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{3}-\beta _{1}q^{5}+2q^{7}+(3+\cdots)q^{9}+\cdots\)
2368.2.g.i	$2368$	$2$	2368.g	37.b	$2$	$4$	$4$	$18.909$	\(\Q(i, \sqrt{37})\)	\(\Q(\sqrt{-37}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{9}+\beta _{1}q^{19}+(-\beta _{1}-\beta _{2})q^{23}+\cdots\)
2368.2.g.j	$2368$	$2$	2368.g	37.b	$2$	$4$	$4$	$18.909$	\(\Q(i, \sqrt{21})\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-8\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{3}+\beta _{1}q^{5}-2q^{7}+(3-\beta _{3})q^{9}+\cdots\)
2368.2.g.k	$2368$	$2$	2368.g	37.b	$2$	$6$	$6$	$18.909$	6.0.3356224.1	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(14\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{3}+(-\beta _{1}+\beta _{2}-\beta _{5})q^{5}+\cdots\)
2368.2.g.l	$2368$	$2$	2368.g	37.b	$2$	$6$	$6$	$18.909$	6.0.3356224.1	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-14\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+\beta _{5})q^{5}+(-2+\cdots)q^{7}+\cdots\)
2368.2.g.m	$2368$	$2$	2368.g	37.b	$2$	$8$	$8$	$18.909$	8.0.2992527616.3	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(12\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{4})q^{3}-\beta _{6}q^{5}+(1-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
2368.2.g.n	$2368$	$2$	2368.g	37.b	$2$	$8$	$8$	$18.909$	8.0.2992527616.3	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(-12\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{4})q^{3}-\beta _{6}q^{5}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
2368.2.g.o	$2368$	$2$	2368.g	37.b	$2$	$10$	$10$	$18.909$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{7}q^{5}-\beta _{3}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
2368.2.g.p	$2368$	$2$	2368.g	37.b	$2$	$10$	$10$	$18.909$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(4\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{7}q^{5}+\beta _{3}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1184, [\chi])\)\(^{\oplus 2}\)