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

• Label: 2400.2.m
• Level: $2400$
• Weight: $2$
• Character orbit: 2400.m
• Rep. character: $\chi_{2400}(1199,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $5$
• 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.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 120 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(960\)
Trace bound:			\(21\)
Distinguishing \(T_p\):			\(7\), \(11\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	528	76	452
Cusp forms	432	68	364
Eisenstein series	96	8	88

Trace form

\( 68 q + 4 q^{9} + O(q^{10}) \)

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.m.a	$2400$	$2$	2400.m	120.m	$2$	$4$	$4$	$19.164$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-2}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{8}^{2}q^{3}+(1+\zeta_{8}^{3})q^{9}+\zeta_{8}^{3}q^{11}+\cdots\)
2400.2.m.b	$2400$	$2$	2400.m	120.m	$2$	$8$	$8$	$19.164$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-2}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{5}-\zeta_{24}^{6})q^{9}+\cdots\)
2400.2.m.c	$2400$	$2$	2400.m	120.m	$2$	$16$	$16$	$19.164$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+\beta _{9}q^{7}+\beta _{7}q^{9}+\beta _{10}q^{11}+\cdots\)
2400.2.m.d	$2400$	$2$	2400.m	120.m	$2$	$16$	$16$	$19.164$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+\beta _{9}q^{7}+\beta _{7}q^{9}+\beta _{10}q^{11}+\cdots\)
2400.2.m.e	$2400$	$2$	2400.m	120.m	$2$	$24$	$24$	$19.164$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)