Space of modular forms of level 2400, weight 2, and Character 2400.o

• Label: 2400.2.o
• Level: $2400$
• Weight: $2$
• Character orbit: 2400.o
• Rep. character: $\chi_{2400}(2399,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $12$
• Sturm bound: $960$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2400.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(960\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2400, [\chi])\).

	Total	New	Old
Modular forms	528	72	456
Cusp forms	432	72	360
Eisenstein series	96	0	96

Trace form

\( 72 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2400, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2400.2.o.a	$2400$	$2$	2400.o	60.h	$2$	$4$	$4$	$19.164$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{8}^{2})q^{3}+2q^{7}+(-1+2\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
2400.2.o.b	$2400$	$2$	2400.o	60.h	$2$	$4$	$4$	$19.164$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+(2-\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\)
2400.2.o.c	$2400$	$2$	2400.o	60.h	$2$	$4$	$4$	$19.164$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+(2-\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\)
2400.2.o.d	$2400$	$2$	2400.o	60.h	$2$	$4$	$4$	$19.164$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{3}+(-2-\zeta_{8}-\zeta_{8}^{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
2400.2.o.e	$2400$	$2$	2400.o	60.h	$2$	$4$	$4$	$19.164$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{3}+(-2-\zeta_{8}-\zeta_{8}^{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
2400.2.o.f	$2400$	$2$	2400.o	60.h	$2$	$4$	$4$	$19.164$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{3}+(2-\zeta_{8}-\zeta_{8}^{2})q^{7}+(1+\zeta_{8}^{3})q^{9}+\cdots\)
2400.2.o.g	$2400$	$2$	2400.o	60.h	$2$	$4$	$4$	$19.164$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{3}+(2+\zeta_{8}+\zeta_{8}^{2})q^{7}+(1-\zeta_{8}^{3})q^{9}+\cdots\)
2400.2.o.h	$2400$	$2$	2400.o	60.h	$2$	$4$	$4$	$19.164$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(-8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{2})q^{3}-2q^{7}+(-1+2\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
2400.2.o.i	$2400$	$2$	2400.o	60.h	$2$	$4$	$4$	$19.164$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2-\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\)
2400.2.o.j	$2400$	$2$	2400.o	60.h	$2$	$4$	$4$	$19.164$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2-\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\)
2400.2.o.k	$2400$	$2$	2400.o	60.h	$2$	$16$	$16$	$19.164$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{3}-\beta _{13}q^{7}+(\beta _{9}-\beta _{13})q^{9}+\cdots\)
2400.2.o.l	$2400$	$2$	2400.o	60.h	$2$	$16$	$16$	$19.164$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{3}+\beta _{13}q^{7}+(\beta _{9}-\beta _{13})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)