Space of modular forms of level 48, weight 24, and trivial character

• Label: 48.24.a
• Level: $48$
• Weight: $24$
• Character orbit: 48.a
• Rep. character: $\chi_{48}(1,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $12$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	48.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(48))\).

	Total	New	Old
Modular forms	190	23	167
Cusp forms	178	23	155
Eisenstein series	12	0	12

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(6\)
\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(+\)	$-$	\(6\)
\(-\)	\(-\)	$+$	\(6\)
Plus space		\(+\)	\(12\)
Minus space		\(-\)	\(11\)

Trace form

\( 23 q - 177147 q^{3} - 35553398 q^{5} + 27593280 q^{7} + 721764371007 q^{9} + O(q^{10}) \)

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(48))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3
48.24.a.a	$48$	$24$	48.a	1.a	$1$	$1$	$1$	$160.898$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-177147\)	\(-48863730\)	\(1723688680\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{11}q^{3}-48863730q^{5}+1723688680q^{7}+\cdots\)
48.24.a.b	$48$	$24$	48.a	1.a	$1$	$1$	$1$	$160.898$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-177147\)	\(-35483250\)	\(2385847912\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{11}q^{3}-35483250q^{5}+2385847912q^{7}+\cdots\)
48.24.a.c	$48$	$24$	48.a	1.a	$1$	$1$	$1$	$160.898$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(177147\)	\(-9019770\)	\(-515282432\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{11}q^{3}-9019770q^{5}-515282432q^{7}+\cdots\)
48.24.a.d	$48$	$24$	48.a	1.a	$1$	$1$	$1$	$160.898$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(177147\)	\(196251270\)	\(8131131904\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{11}q^{3}+196251270q^{5}+8131131904q^{7}+\cdots\)
48.24.a.e	$48$	$24$	48.a	1.a	$1$	$2$	$2$	$160.898$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-354294\)	\(25248156\)	\(-5764462768\)		$-$	$+$	$-$	$2^{7}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q-3^{11}q^{3}+(12624078-\beta )q^{5}+(-2882231384+\cdots)q^{7}+\cdots\)
48.24.a.f	$48$	$24$	48.a	1.a	$1$	$2$	$2$	$160.898$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-354294\)	\(73907100\)	\(1531228496\)		$-$	$+$	$-$	$2^{7}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q-3^{11}q^{3}+(36953550-\beta )q^{5}+(765614248+\cdots)q^{7}+\cdots\)
48.24.a.g	$48$	$24$	48.a	1.a	$1$	$2$	$2$	$160.898$	\(\Q(\sqrt{530401}) \)	None	✓	$1$	$0$	\(0\)	\(354294\)	\(-46808820\)	\(211963904\)		$-$	$-$	$+$	$2^{9}\cdot 3$	$\mathrm{SU}(2)$	\(q+3^{11}q^{3}+(-23404410-245\beta )q^{5}+\cdots\)
48.24.a.h	$48$	$24$	48.a	1.a	$1$	$2$	$2$	$160.898$	\(\Q(\sqrt{1792561}) \)	None	✓	$1$	$0$	\(0\)	\(354294\)	\(-34222068\)	\(-21634816\)		$-$	$-$	$+$	$2^{8}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+3^{11}q^{3}+(-17111034-19\beta )q^{5}+\cdots\)
48.24.a.i	$48$	$24$	48.a	1.a	$1$	$2$	$2$	$160.898$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(354294\)	\(2075980\)	\(-4451754048\)		$+$	$-$	$-$	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+3^{11}q^{3}+(1037990-5\beta )q^{5}+(-2225877024+\cdots)q^{7}+\cdots\)
48.24.a.j	$48$	$24$	48.a	1.a	$1$	$3$	$3$	$160.898$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-531441\)	\(-45012150\)	\(-281292072\)		$+$	$+$	$+$	$2^{21}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)$	\(q-3^{11}q^{3}+(-15004050-\beta _{1})q^{5}+\cdots\)
48.24.a.k	$48$	$24$	48.a	1.a	$1$	$3$	$3$	$160.898$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-531441\)	\(-36400950\)	\(418786392\)		$+$	$+$	$+$	$2^{21}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)$	\(q-3^{11}q^{3}+(-12133650-\beta _{1})q^{5}+\cdots\)
48.24.a.l	$48$	$24$	48.a	1.a	$1$	$3$	$3$	$160.898$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(531441\)	\(-77225166\)	\(-3340627872\)		$+$	$-$	$-$	$2^{21}\cdot 3^{5}$	$\mathrm{SU}(2)$	\(q+3^{11}q^{3}+(-25741722+\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(48))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(48)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)