Space of modular forms of level 2320, weight 2, and Character 2320.d

• Label: 2320.2.d
• Level: $2320$
• Weight: $2$
• Character orbit: 2320.d
• Rep. character: $\chi_{2320}(929,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $11$
• Sturm bound: $720$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2320 = 2^{4} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2320.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(720\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2320, [\chi])\).

	Total	New	Old
Modular forms	372	84	288
Cusp forms	348	84	264
Eisenstein series	24	0	24

Trace form

84 * q - 84 * q^9 - 12 * q^11 + 12 * q^15 + 20 * q^19 + 4 * q^31 - 24 * q^35 - 16 * q^39 - 8 * q^41 - 76 * q^49 - 8 * q^51 + 4 * q^55 + 16 * q^59 + 16 * q^61 - 16 * q^65 - 16 * q^69 - 16 * q^71 + 28 * q^75 - 60 * q^79 + 116 * q^81 + 16 * q^85 + 8 * q^89 + 32 * q^91 + 8 * q^95 + 68 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2320, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2320.2.d.a	$2320$	$2$	2320.d	5.b	$2$	$2$	$2$	$18.525$	\(\Q(\sqrt{-1}) \)	None					1160.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+(\beta-1)q^{5}+\beta q^{7}-q^{9}+\cdots\)
2320.2.d.b	$2320$	$2$	2320.d	5.b	$2$	$2$	$2$	$18.525$	\(\Q(\sqrt{-1}) \)	None					1160.2.d.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta+1)q^{5}+\beta q^{7}+3 q^{9}+3\beta q^{17}+\cdots\)
2320.2.d.c	$2320$	$2$	2320.d	5.b	$2$	$4$	$4$	$18.525$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					145.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2320.2.d.d	$2320$	$2$	2320.d	5.b	$2$	$4$	$4$	$18.525$	\(\Q(i, \sqrt{5})\)	None					290.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
2320.2.d.e	$2320$	$2$	2320.d	5.b	$2$	$4$	$4$	$18.525$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None					580.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+\cdots\)
2320.2.d.f	$2320$	$2$	2320.d	5.b	$2$	$4$	$4$	$18.525$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None					145.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{3}q^{7}+q^{9}+\cdots\)
2320.2.d.g	$2320$	$2$	2320.d	5.b	$2$	$6$	$6$	$18.525$	6.0.84345856.2	None					145.2.b.c	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{1}q^{5}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
2320.2.d.h	$2320$	$2$	2320.d	5.b	$2$	$10$	$10$	$18.525$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					290.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}+\beta _{5}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
2320.2.d.i	$2320$	$2$	2320.d	5.b	$2$	$10$	$10$	$18.525$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					580.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{8}q^{5}+(-\beta _{1}+\beta _{8}+\beta _{9})q^{7}+\cdots\)
2320.2.d.j	$2320$	$2$	2320.d	5.b	$2$	$16$	$16$	$18.525$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					1160.2.d.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{8}q^{5}-\beta _{13}q^{7}+(-1+\beta _{9}+\cdots)q^{9}+\cdots\)
2320.2.d.k	$2320$	$2$	2320.d	5.b	$2$	$22$	$22$	$18.525$		None			✓		1160.2.d.d	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(580, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1160, [\chi])\)\(^{\oplus 2}\)