Space of modular forms of level 2432, weight 2, and Character 2432.c

• Label: 2432.2.c
• Level: $2432$
• Weight: $2$
• Character orbit: 2432.c
• Rep. character: $\chi_{2432}(1217,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $10$
• Sturm bound: $640$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2432 = 2^{7} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2432.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(640\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2432, [\chi])\).

	Total	New	Old
Modular forms	336	72	264
Cusp forms	304	72	232
Eisenstein series	32	0	32

Trace form

\( 72 q - 72 q^{9} - 16 q^{17} - 56 q^{25} + 16 q^{41} + 72 q^{49} - 64 q^{65} + 48 q^{73} + 8 q^{81} + 112 q^{89} + 48 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2432, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2432.2.c.a	$2432$	$2$	2432.c	8.b	$2$	$2$	$2$	$19.420$	\(\Q(\sqrt{-1}) \)	None		✓			2432.2.c.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 i q^{5}-q^{7}+2 q^{9}-4 i q^{11}+\cdots\)
2432.2.c.b	$2432$	$2$	2432.c	8.b	$2$	$2$	$2$	$19.420$	\(\Q(\sqrt{-1}) \)	None		✓			2432.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-2 i q^{5}+q^{7}+2 q^{9}-4 i q^{11}+\cdots\)
2432.2.c.c	$2432$	$2$	2432.c	8.b	$2$	$4$	$4$	$19.420$	\(\Q(\zeta_{12})\)	None		✓			2432.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{3}+2\beta_1 q^{5}+(-\beta_{3}-1)q^{7}+\cdots\)
2432.2.c.d	$2432$	$2$	2432.c	8.b	$2$	$4$	$4$	$19.420$	\(\Q(\zeta_{12})\)	None		✓			2432.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{3}-2\beta_1 q^{5}+(-\beta_{3}+1)q^{7}+\cdots\)
2432.2.c.e	$2432$	$2$	2432.c	8.b	$2$	$6$	$6$	$19.420$	6.0.399424.1	None		✓			2432.2.c.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}+\beta _{4}+\beta _{5})q^{3}+(-\beta _{2}-\beta _{5})q^{5}+\cdots\)
2432.2.c.f	$2432$	$2$	2432.c	8.b	$2$	$6$	$6$	$19.420$	6.0.3182656.1	None		✓			2432.2.c.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)
2432.2.c.g	$2432$	$2$	2432.c	8.b	$2$	$6$	$6$	$19.420$	6.0.3182656.1	None		✓			2432.2.c.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}+(-\beta _{4}-\beta _{5})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
2432.2.c.h	$2432$	$2$	2432.c	8.b	$2$	$6$	$6$	$19.420$	6.0.399424.1	None		✓			2432.2.c.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}+\beta _{4}+\beta _{5})q^{3}+(\beta _{2}+\beta _{5})q^{5}+\cdots\)
2432.2.c.i	$2432$	$2$	2432.c	8.b	$2$	$16$	$16$	$19.420$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			2432.2.c.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{3}+\beta _{7}q^{5}+\beta _{10}q^{7}+(\beta _{12}-\beta _{13}+\cdots)q^{9}+\cdots\)
2432.2.c.j	$2432$	$2$	2432.c	8.b	$2$	$20$	$20$	$19.420$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		2432.2.c.j	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}-\beta _{15}q^{5}+(-\beta _{17}-\beta _{19})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2432, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2432, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1216, [\chi])\)\(^{\oplus 2}\)