Space of modular forms of level 2448, weight 2, and Character 2448.o

• Label: 2448.2.o
• Level: $2448$
• Weight: $2$
• Character orbit: 2448.o
• Rep. character: $\chi_{2448}(2447,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $4$
• Sturm bound: $864$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2448.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 204 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(864\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2448, [\chi])\).

	Total	New	Old
Modular forms	456	36	420
Cusp forms	408	36	372
Eisenstein series	48	0	48

Trace form

\( 36 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2448, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2448.2.o.a	$2448$	$2$	2448.o	204.h	$2$	$4$	$4$	$19.547$	\(\Q(\sqrt{-2}, \sqrt{-7})\)	None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{5}+\beta _{1}q^{7}+\beta _{3}q^{11}+3q^{13}+\cdots\)
2448.2.o.b	$2448$	$2$	2448.o	204.h	$2$	$4$	$4$	$19.547$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{8}^{3}q^{5}-4q^{13}+(-\zeta_{8}^{2}-2\zeta_{8}^{3})q^{17}+\cdots\)
2448.2.o.c	$2448$	$2$	2448.o	204.h	$2$	$4$	$4$	$19.547$	\(\Q(\sqrt{-2}, \sqrt{-7})\)	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}+3q^{13}+\cdots\)
2448.2.o.d	$2448$	$2$	2448.o	204.h	$2$	$24$	$24$	$19.547$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2448, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1224, [\chi])\)\(^{\oplus 2}\)