Space of modular forms of level 48, weight 10, and Character 48.c

• Label: 48.10.c
• Level: $48$
• Weight: $10$
• Character orbit: 48.c
• Rep. character: $\chi_{48}(47,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $3$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	48.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(80\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(48, [\chi])\).

	Total	New	Old
Modular forms	78	18	60
Cusp forms	66	18	48
Eisenstein series	12	0	12

Trace form

\( 18 q + 41610 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(48, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
48.10.c.a	$48$	$10$	48.c	12.b	$2$	$2$	$2$	$24.722$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q-3\zeta_{6}q^{3}+38\zeta_{6}q^{7}-3^{9}q^{9}-118370q^{13}+\cdots\)
48.10.c.b	$48$	$10$	48.c	12.b	$2$	$4$	$4$	$24.722$	\(\Q(\sqrt{-51}, \sqrt{534})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+77\beta _{2}q^{7}+(18765+\cdots)q^{9}+\cdots\)
48.10.c.c	$48$	$10$	48.c	12.b	$2$	$12$	$12$	$24.722$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{72}\cdot 3^{23}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{1}q^{5}+(\beta _{2}+3\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(48, [\chi]) \cong \)