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

• Label: 2448.2.c
• Level: $2448$
• Weight: $2$
• Character orbit: 2448.c
• Rep. character: $\chi_{2448}(577,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $18$
• Sturm bound: $864$
• Trace bound: $35$

Defining parameters

Level:	\( N \)	\(=\)	\( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2448.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(864\)
Trace bound:			\(35\)
Distinguishing \(T_p\):			\(5\), \(7\), \(47\)

Dimensions

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

	Total	New	Old
Modular forms	456	46	410
Cusp forms	408	44	364
Eisenstein series	48	2	46

Trace form

\( 44 q + O(q^{10}) \)

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.c.a	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-iq^{7}-6q^{13}+(1+2i)q^{17}+\cdots\)
2448.2.c.b	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{5}+4iq^{7}-iq^{11}-5q^{13}+\cdots\)
2448.2.c.c	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{5}-4iq^{7}-iq^{11}-5q^{13}+\cdots\)
2448.2.c.d	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}-3\beta q^{7}+\beta q^{11}-4q^{13}+\cdots\)
2448.2.c.e	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}-iq^{11}-2q^{13}+(-1-2i)q^{17}+\cdots\)
2448.2.c.f	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{5}+2iq^{7}+5iq^{11}-q^{13}+\cdots\)
2448.2.c.g	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-17}) \)	\(\Q(\sqrt{-51}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-\beta q^{11}-q^{13}-\beta q^{17}-5q^{19}+\cdots\)
2448.2.c.h	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+\beta q^{7}+2\beta q^{11}+2q^{13}+(-3+\cdots)q^{17}+\cdots\)
2448.2.c.i	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-3\beta q^{7}+2\beta q^{11}+2q^{13}+\cdots\)
2448.2.c.j	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}+iq^{11}+2q^{13}+(-1-i)q^{17}+\cdots\)
2448.2.c.k	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+3\beta q^{7}+2\beta q^{11}+2q^{13}+\cdots\)
2448.2.c.l	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-\beta q^{7}+2\beta q^{11}+2q^{13}+(3+\cdots)q^{17}+\cdots\)
2448.2.c.m	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+\beta q^{7}+2\beta q^{11}+2q^{13}+(3+\cdots)q^{17}+\cdots\)
2448.2.c.n	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-\beta q^{11}+2q^{13}+(3-\beta )q^{17}+\cdots\)
2448.2.c.o	$2448$	$2$	2448.c	17.b	$2$	$2$	$2$	$19.547$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+2iq^{7}-3iq^{11}+3q^{13}+\cdots\)
2448.2.c.p	$2448$	$2$	2448.c	17.b	$2$	$4$	$4$	$19.547$	\(\Q(i, \sqrt{17})\)	\(\Q(\sqrt{-51}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{5}+(-\beta _{1}-2\beta _{2})q^{11}+(1-\beta _{3})q^{13}+\cdots\)
2448.2.c.q	$2448$	$2$	2448.c	17.b	$2$	$4$	$4$	$19.547$	\(\Q(i, \sqrt{33})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+\beta _{1}q^{11}+\cdots\)
2448.2.c.r	$2448$	$2$	2448.c	17.b	$2$	$6$	$6$	$19.547$	6.0.399424.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\beta _{5}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 5}\)