Space of modular forms of level 2450, weight 2, and Character 2450.c

• Label: 2450.2.c
• Level: $2450$
• Weight: $2$
• Character orbit: 2450.c
• Rep. character: $\chi_{2450}(99,\cdot)$
• Character field: $\Q$
• Dimension: $62$
• Newform subspaces: $24$
• Sturm bound: $840$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2450.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(840\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(3\), \(11\), \(13\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2450, [\chi])\).

	Total	New	Old
Modular forms	468	62	406
Cusp forms	372	62	310
Eisenstein series	96	0	96

Trace form

\( 62 q - 62 q^{4} + 2 q^{6} - 80 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2450, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2450.2.c.a	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{8}+\cdots\)
2450.2.c.b	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.c	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.d	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.e	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.f	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots\)
2450.2.c.g	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}+2q^{9}+\cdots\)
2450.2.c.h	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}+2q^{9}+\cdots\)
2450.2.c.i	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{8}+3q^{9}-2q^{11}+\cdots\)
2450.2.c.j	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{8}+3q^{9}-2q^{11}+\cdots\)
2450.2.c.k	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{8}+3q^{9}+4q^{11}+\cdots\)
2450.2.c.l	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}+2q^{9}+\cdots\)
2450.2.c.m	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}+2q^{9}+\cdots\)
2450.2.c.n	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.o	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.p	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.q	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
2450.2.c.r	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+3iq^{3}-q^{4}+3q^{6}+iq^{8}+\cdots\)
2450.2.c.s	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+3iq^{3}-q^{4}+3q^{6}+iq^{8}+\cdots\)
2450.2.c.t	$2450$	$2$	2450.c	5.b	$2$	$4$	$4$	$19.563$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{2}+(2\zeta_{8}-\zeta_{8}^{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots\)
2450.2.c.u	$2450$	$2$	2450.c	5.b	$2$	$4$	$4$	$19.563$	\(\Q(i, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{1}q^{8}+\cdots\)
2450.2.c.v	$2450$	$2$	2450.c	5.b	$2$	$4$	$4$	$19.563$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots\)
2450.2.c.w	$2450$	$2$	2450.c	5.b	$2$	$4$	$4$	$19.563$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{2}+(2\zeta_{8}-\zeta_{8}^{2})q^{3}-q^{4}+(2+\cdots)q^{6}+\cdots\)
2450.2.c.x	$2450$	$2$	2450.c	5.b	$2$	$8$	$8$	$19.563$	8.0.959512576.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{3}-\beta _{7})q^{3}-q^{4}+\beta _{6}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)