Space of modular forms of level 2352, weight 2, and Character 2352.q

• Label: 2352.2.q
• Level: $2352$
• Weight: $2$
• Character orbit: 2352.q
• Rep. character: $\chi_{2352}(961,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $33$
• Sturm bound: $896$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2352.q (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 33 \)
Sturm bound:			\(896\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

	Total	New	Old
Modular forms	992	80	912
Cusp forms	800	80	720
Eisenstein series	192	0	192

Trace form

80 * q + 2 * q^3 - 40 * q^9 - 8 * q^11 + 10 * q^19 - 20 * q^23 - 36 * q^25 - 4 * q^27 - 32 * q^29 - 14 * q^31 + 4 * q^33 + 16 * q^37 - 2 * q^39 - 16 * q^41 + 20 * q^43 + 12 * q^47 + 24 * q^53 + 56 * q^55 + 8 * q^57 + 16 * q^59 + 8 * q^61 + 8 * q^65 + 2 * q^67 - 16 * q^71 - 12 * q^73 + 14 * q^75 - 22 * q^79 - 40 * q^81 + 24 * q^83 + 32 * q^85 - 12 * q^87 - 16 * q^89 - 16 * q^93 + 60 * q^95 - 8 * q^97 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2352.2.q.a	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					294.2.a.b	$2$	$0$	\(0\)	\(-1\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.b	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					84.2.a.a	$2$	$1$	\(0\)	\(-1\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.c	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					21.2.e.a	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.d	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					168.2.a.a	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.e	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					21.2.a.a	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.f	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					168.2.q.a	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots\)
2352.2.q.g	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					84.2.a.b	$2$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-6+6\zeta_{6})q^{11}+\cdots\)
2352.2.q.h	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					1176.2.a.b	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+(4+\cdots)q^{17}+\cdots\)
2352.2.q.i	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					42.2.a.a	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.j	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					168.2.a.b	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.k	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					588.2.a.b	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.l	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					24.2.a.a	$2$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.m	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					42.2.e.b	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
2352.2.q.n	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					42.2.a.a	$2$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
2352.2.q.o	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					168.2.a.b	$2$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}-2q^{13}+\cdots\)
2352.2.q.p	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					588.2.a.b	$2$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.q	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					84.2.i.a	$2$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.r	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					24.2.a.a	$2$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
2352.2.q.s	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					84.2.a.b	$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(-6+6\zeta_{6})q^{11}+\cdots\)
2352.2.q.t	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					1176.2.a.b	$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(-4+\cdots)q^{17}+\cdots\)
2352.2.q.u	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					42.2.e.a	$2$	$0$	\(0\)	\(1\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}-\zeta_{6}q^{9}+(5-5\zeta_{6})q^{11}+\cdots\)
2352.2.q.v	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					168.2.q.b	$2$	$0$	\(0\)	\(1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
2352.2.q.w	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					168.2.a.a	$2$	$0$	\(0\)	\(1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}-6q^{13}+\cdots\)
2352.2.q.x	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					21.2.a.a	$2$	$0$	\(0\)	\(1\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(4+\cdots)q^{11}+\cdots\)
2352.2.q.y	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					294.2.a.b	$2$	$0$	\(0\)	\(1\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
2352.2.q.z	$2352$	$2$	2352.q	7.c	$3$	$2$	$1$	$18.781$	\(\Q(\sqrt{-3}) \)	None					84.2.a.a	$2$	$0$	\(0\)	\(1\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(2+\cdots)q^{11}+\cdots\)
2352.2.q.ba	$2352$	$2$	2352.q	7.c	$3$	$4$	$2$	$18.781$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					1176.2.a.l	$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bb	$2352$	$2$	2352.q	7.c	$3$	$4$	$2$	$18.781$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					147.2.a.d	$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bc	$2352$	$2$	2352.q	7.c	$3$	$4$	$2$	$18.781$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					1176.2.a.j	$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bd	$2352$	$2$	2352.q	7.c	$3$	$4$	$2$	$18.781$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					147.2.a.d	$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.be	$2352$	$2$	2352.q	7.c	$3$	$4$	$2$	$18.781$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					1176.2.a.j	$2$	$0$	\(0\)	\(2\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
2352.2.q.bf	$2352$	$2$	2352.q	7.c	$3$	$4$	$2$	$18.781$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None					168.2.q.c	$2$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{9}+\cdots\)
2352.2.q.bg	$2352$	$2$	2352.q	7.c	$3$	$4$	$2$	$18.781$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					1176.2.a.l	$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)