Space of modular forms of level 2850, weight 2, and Character 2850.d

• Label: 2850.2.d
• Level: $2850$
• Weight: $2$
• Character orbit: 2850.d
• Rep. character: $\chi_{2850}(799,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $24$
• Sturm bound: $1200$
• Trace bound: $26$

Defining parameters

Level:	\( N \)	\(=\)	\( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2850.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(1200\)
Trace bound:			\(26\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2850, [\chi])\).

	Total	New	Old
Modular forms	624	56	568
Cusp forms	576	56	520
Eisenstein series	48	0	48

Trace form

\( 56 q - 56 q^{4} + 4 q^{6} - 56 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2850, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2850.2.d.a	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2850.2.d.b	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{9}+\cdots\)
2850.2.d.c	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2850.2.d.d	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2850.2.d.e	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2850.2.d.f	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2850.2.d.g	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
2850.2.d.h	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2850.2.d.i	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{9}+\cdots\)
2850.2.d.j	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.k	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
2850.2.d.l	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.m	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.n	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.o	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
2850.2.d.p	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
2850.2.d.q	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.r	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.s	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
2850.2.d.t	$2850$	$2$	2850.d	5.b	$2$	$2$	$2$	$22.757$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.u	$2850$	$2$	2850.d	5.b	$2$	$4$	$4$	$22.757$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}-q^{4}-q^{6}+(\zeta_{12}+\cdots)q^{7}+\cdots\)
2850.2.d.v	$2850$	$2$	2850.d	5.b	$2$	$4$	$4$	$22.757$	\(\Q(i, \sqrt{10})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}-q^{6}+\beta _{2}q^{7}+\cdots\)
2850.2.d.w	$2850$	$2$	2850.d	5.b	$2$	$4$	$4$	$22.757$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}+q^{6}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
2850.2.d.x	$2850$	$2$	2850.d	5.b	$2$	$4$	$4$	$22.757$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}-q^{4}+q^{6}+(\zeta_{12}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)