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

• Label: 2400.2.w
• Level: $2400$
• Weight: $2$
• Character orbit: 2400.w
• Rep. character: $\chi_{2400}(607,\cdot)$
• Character field: $\Q(\zeta_{4})$
• 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.w (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(960\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	1056	72	984
Cusp forms	864	72	792
Eisenstein series	192	0	192

Trace form

\( 72 q + 8 q^{13} - 24 q^{17} - 16 q^{33} - 8 q^{37} - 64 q^{41} - 8 q^{53} + 40 q^{73} + 96 q^{77} - 72 q^{81} + 32 q^{93} - 24 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2400.2.w.a	$2400$	$2$	2400.w	20.e	$4$	$4$	$2$	$19.164$	\(\Q(\zeta_{8})\)	None		✓			2400.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{3}+(-2+2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{7}+\cdots\)
2400.2.w.b	$2400$	$2$	2400.w	20.e	$4$	$4$	$2$	$19.164$	\(\Q(\zeta_{8})\)	None		✓			2400.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{3}+(-2+2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{7}+\cdots\)
2400.2.w.c	$2400$	$2$	2400.w	20.e	$4$	$4$	$2$	$19.164$	\(\Q(\zeta_{8})\)	None					480.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{3}+(-1+\zeta_{8}^{2})q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
2400.2.w.d	$2400$	$2$	2400.w	20.e	$4$	$4$	$2$	$19.164$	\(\Q(\zeta_{8})\)	None					480.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{3}+(1-\zeta_{8}^{2})q^{7}+\zeta_{8}^{2}q^{9}+(-\zeta_{8}+\cdots)q^{11}+\cdots\)
2400.2.w.e	$2400$	$2$	2400.w	20.e	$4$	$4$	$2$	$19.164$	\(\Q(\zeta_{8})\)	None		✓			2400.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{3}+(2-2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
2400.2.w.f	$2400$	$2$	2400.w	20.e	$4$	$4$	$2$	$19.164$	\(\Q(\zeta_{8})\)	None		✓			2400.2.w.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}q^{3}+(2-2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
2400.2.w.g	$2400$	$2$	2400.w	20.e	$4$	$8$	$4$	$19.164$	\(\Q(\zeta_{24})\)	None		✓			2400.2.w.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_1 q^{3}+(\beta_{6}-\beta_{5}-\beta_{4}+\cdots-1)q^{7}+\cdots\)
2400.2.w.h	$2400$	$2$	2400.w	20.e	$4$	$8$	$4$	$19.164$	\(\Q(\zeta_{24})\)	None		✓			2400.2.w.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_1 q^{3}+(\beta_{6}-\beta_{5}-\beta_{4}+\cdots-1)q^{7}+\cdots\)
2400.2.w.i	$2400$	$2$	2400.w	20.e	$4$	$8$	$4$	$19.164$	8.0.1698758656.6	None					480.2.w.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{3}+(-1-\beta _{4}-\beta _{6})q^{7}-\beta _{4}q^{9}+\cdots\)
2400.2.w.j	$2400$	$2$	2400.w	20.e	$4$	$8$	$4$	$19.164$	8.0.1698758656.6	None					480.2.w.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{3}+(1+\beta _{5})q^{7}+\beta _{4}q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2400.2.w.k	$2400$	$2$	2400.w	20.e	$4$	$8$	$4$	$19.164$	\(\Q(\zeta_{24})\)	None		✓			2400.2.w.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_1 q^{3}+(-\beta_{6}-\beta_{5}+\beta_{4}+\cdots+1)q^{7}+\cdots\)
2400.2.w.l	$2400$	$2$	2400.w	20.e	$4$	$8$	$4$	$19.164$	\(\Q(\zeta_{24})\)	None		✓			2400.2.w.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_1 q^{3}+(-\beta_{6}-\beta_{5}+\beta_{4}+\cdots+1)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)