Space of modular forms of level 48, weight 25, and Character 48.e

• Label: 48.25.e
• Level: $48$
• Weight: $25$
• Character orbit: 48.e
• Rep. character: $\chi_{48}(17,\cdot)$
• Character field: $\Q$
• Dimension: $47$
• Newform subspaces: $5$
• Sturm bound: $200$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 25 \)
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:			\(200\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{25}(48, [\chi])\).

	Total	New	Old
Modular forms	198	49	149
Cusp forms	186	47	139
Eisenstein series	12	2	10

Trace form

\( 47 q + q^{3} - 15804565918 q^{7} + 190663580239 q^{9} + O(q^{10}) \)

Decomposition of \(S_{25}^{\mathrm{new}}(48, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
48.25.e.a	$48$	$25$	48.e	3.b	$2$	$1$	$1$	$175.184$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-531441\)	\(0\)	\(4119710398\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{12}q^{3}+4119710398q^{7}+3^{24}q^{9}+\cdots\)
48.25.e.b	$48$	$25$	48.e	3.b	$2$	$6$	$6$	$175.184$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(616842\)	\(0\)	\(-1988064876\)	$2^{28}\cdot 3^{24}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(102807+\beta _{2})q^{3}+(29\beta _{1}+143\beta _{2}+\cdots)q^{5}+\cdots\)
48.25.e.c	$48$	$25$	48.e	3.b	$2$	$8$	$8$	$175.184$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-519960\)	\(0\)	\(-10911959920\)	$2^{50}\cdot 3^{38}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-64995+\beta _{1})q^{3}+(53\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
48.25.e.d	$48$	$25$	48.e	3.b	$2$	$8$	$8$	$175.184$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(131880\)	\(0\)	\(10160794640\)	$2^{60}\cdot 3^{34}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(16485-\beta _{1})q^{3}+(155\beta _{1}-145\beta _{2}+\cdots)q^{5}+\cdots\)
48.25.e.e	$48$	$25$	48.e	3.b	$2$	$24$	$24$	$175.184$		None		$2$	$0$	\(0\)	\(302680\)	\(0\)	\(-17185046160\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{25}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{25}^{\mathrm{old}}(48, [\chi]) \cong \) \(S_{25}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{25}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{25}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{25}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)