Space of modular forms of level 2400, weight 3, and Character 2400.e

• Label: 2400.3.e
• Level: $2400$
• Weight: $3$
• Character orbit: 2400.e
• Rep. character: $\chi_{2400}(1951,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $9$
• Sturm bound: $1440$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2400.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1440\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2400, [\chi])\).

	Total	New	Old
Modular forms	1008	76	932
Cusp forms	912	76	836
Eisenstein series	96	0	96

Trace form

76 * q - 228 * q^9 - 8 * q^13 + 24 * q^17 - 48 * q^21 + 40 * q^29 + 48 * q^33 + 88 * q^37 + 88 * q^41 - 532 * q^49 - 88 * q^53 + 48 * q^57 + 24 * q^61 - 40 * q^73 - 256 * q^77 + 684 * q^81 + 376 * q^89 + 48 * q^93 + 280 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(2400, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2400.3.e.a	$2400$	$3$	2400.e	4.b	$2$	$4$	$4$	$65.395$	\(\Q(\zeta_{12})\)	None					96.3.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{3}+(-4\beta_{2}+\beta_1)q^{7}-3 q^{9}+\cdots\)
2400.3.e.b	$2400$	$3$	2400.e	4.b	$2$	$8$	$8$	$65.395$	8.0.\(\cdots\).3	None		✓			2400.3.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+(\beta _{1}-2\beta _{5})q^{7}-3q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2400.3.e.c	$2400$	$3$	2400.e	4.b	$2$	$8$	$8$	$65.395$	8.0.\(\cdots\).3	None		✓			2400.3.e.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{1}q^{7}-3q^{9}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
2400.3.e.d	$2400$	$3$	2400.e	4.b	$2$	$8$	$8$	$65.395$	8.0.\(\cdots\).3	None		✓			2400.3.e.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{1}q^{7}-3q^{9}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
2400.3.e.e	$2400$	$3$	2400.e	4.b	$2$	$8$	$8$	$65.395$	8.0.\(\cdots\).3	None		✓			2400.3.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+(\beta _{1}-2\beta _{5})q^{7}-3q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
2400.3.e.f	$2400$	$3$	2400.e	4.b	$2$	$8$	$8$	$65.395$	8.0.12960000.1	None					480.3.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{3}+\beta _{5})q^{7}-3q^{9}+(-2\beta _{2}+\cdots)q^{11}+\cdots\)
2400.3.e.g	$2400$	$3$	2400.e	4.b	$2$	$8$	$8$	$65.395$	8.0.12960000.1	None					480.3.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(4\beta _{2}-\beta _{3}+\beta _{5})q^{7}-3q^{9}+\cdots\)
2400.3.e.h	$2400$	$3$	2400.e	4.b	$2$	$12$	$12$	$65.395$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					480.3.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{3}-\beta _{4}q^{7}-3q^{9}+(-\beta _{4}-\beta _{11})q^{11}+\cdots\)
2400.3.e.i	$2400$	$3$	2400.e	4.b	$2$	$12$	$12$	$65.395$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					480.3.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{3}-\beta _{4}q^{7}-3q^{9}+(\beta _{4}+\beta _{11})q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(2400, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2400, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)