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

• Label: 2400.2.b
• Level: $2400$
• Weight: $2$
• Character orbit: 2400.b
• Rep. character: $\chi_{2400}(2351,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $9$
• Sturm bound: $960$
• Trace bound: $21$

Defining parameters

Level:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2400.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(960\)
Trace bound:			\(21\)
Distinguishing \(T_p\):			\(7\), \(11\), \(23\), \(43\)

Dimensions

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

	Total	New	Old
Modular forms	528	82	446
Cusp forms	432	70	362
Eisenstein series	96	12	84

Trace form

\( 70 q - 2 q^{3} + 2 q^{9} + O(q^{10}) \)

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.b.a	$2400$	$2$	2400.b	24.f	$2$	$2$	$2$	$19.164$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1+\beta )q^{3}+(-1-2\beta )q^{9}+2\beta q^{11}+\cdots\)
2400.2.b.b	$2400$	$2$	2400.b	24.f	$2$	$4$	$4$	$19.164$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
2400.2.b.c	$2400$	$2$	2400.b	24.f	$2$	$4$	$4$	$19.164$	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{3}-3q^{9}+4\beta _{1}q^{17}+4q^{19}+\cdots\)
2400.2.b.d	$2400$	$2$	2400.b	24.f	$2$	$4$	$4$	$19.164$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(1+\beta _{2})q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{9}+\cdots\)
2400.2.b.e	$2400$	$2$	2400.b	24.f	$2$	$8$	$8$	$19.164$	8.0.1649659456.5	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}-\beta _{2}q^{7}+\beta _{7}q^{9}-\beta _{4}q^{11}+\cdots\)
2400.2.b.f	$2400$	$2$	2400.b	24.f	$2$	$8$	$8$	$19.164$	8.0.1649659456.5	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{7}+(-\beta _{3}-\beta _{5})q^{9}+\cdots\)
2400.2.b.g	$2400$	$2$	2400.b	24.f	$2$	$12$	$12$	$19.164$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{6}q^{7}+(\beta _{1}+\beta _{8})q^{9}+(-\beta _{5}+\cdots)q^{11}+\cdots\)
2400.2.b.h	$2400$	$2$	2400.b	24.f	$2$	$12$	$12$	$19.164$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}-\beta _{6}q^{7}+(\beta _{1}-\beta _{3}+\beta _{5}-\beta _{8}+\cdots)q^{9}+\cdots\)
2400.2.b.i	$2400$	$2$	2400.b	24.f	$2$	$16$	$16$	$19.164$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-\beta _{15}q^{7}+(1+\beta _{8}-\beta _{13}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)