Space of modular forms of level 48, weight 23, and Character 48.e

• Label: 48.23.e
• Level: $48$
• Weight: $23$
• Character orbit: 48.e
• Rep. character: $\chi_{48}(17,\cdot)$
• Character field: $\Q$
• Dimension: $43$
• Newform subspaces: $5$
• Sturm bound: $184$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	48.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(184\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(48, [\chi])\).

	Total	New	Old
Modular forms	182	45	137
Cusp forms	170	43	127
Eisenstein series	12	2	10

Trace form

\( 43 q + q^{3} + 13760730 q^{7} - 20626788077 q^{9} + O(q^{10}) \)

Decomposition of \(S_{23}^{\mathrm{new}}(48, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
48.23.e.a	$48$	$23$	48.e	3.b	$2$	$1$	$1$	$147.220$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(177147\)	\(0\)	\(3954581662\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{11}q^{3}+3954581662q^{7}+3^{22}q^{9}+\cdots\)
48.23.e.b	$48$	$23$	48.e	3.b	$2$	$6$	$6$	$147.220$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(-86670\)	\(0\)	\(3447063060\)	$2^{33}\cdot 3^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-14445-\beta _{2})q^{3}+(10\beta _{1}-2^{4}\beta _{2}+\cdots)q^{5}+\cdots\)
48.23.e.c	$48$	$23$	48.e	3.b	$2$	$6$	$6$	$147.220$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(-56574\)	\(0\)	\(-3018367884\)	$2^{31}\cdot 3^{24}\cdot 5^{2}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-9429+\beta _{1})q^{3}+(15\beta _{1}+\beta _{2})q^{5}+\cdots\)
48.23.e.d	$48$	$23$	48.e	3.b	$2$	$8$	$8$	$147.220$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(69720\)	\(0\)	\(-5645581840\)	$2^{63}\cdot 3^{31}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(8715+\beta _{1})q^{3}+(-\beta _{1}-7\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
48.23.e.e	$48$	$23$	48.e	3.b	$2$	$22$	$22$	$147.220$		None		$2$	$0$	\(0\)	\(-103622\)	\(0\)	\(1276065732\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{23}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{23}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{23}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{23}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{23}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{23}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)