Space of modular forms of level 1850, weight 2, and Character 1850.d

• Label: 1850.2.d
• Level: $1850$
• Weight: $2$
• Character orbit: 1850.d
• Rep. character: $\chi_{1850}(1701,\cdot)$
• Character field: $\Q$
• Dimension: $62$
• Newform subspaces: $9$
• Sturm bound: $570$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(570\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1850, [\chi])\).

	Total	New	Old
Modular forms	298	62	236
Cusp forms	274	62	212
Eisenstein series	24	0	24

Trace form

\( 62 q + 6 q^{3} - 62 q^{4} - 8 q^{7} + 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1850, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1850.2.d.a	$1850$	$2$	1850.d	37.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}-5q^{7}+iq^{8}-3q^{9}+\cdots\)
1850.2.d.b	$1850$	$2$	1850.d	37.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-2q^{7}-iq^{8}-3q^{9}+\cdots\)
1850.2.d.c	$1850$	$2$	1850.d	37.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2q^{7}-iq^{8}-3q^{9}+\cdots\)
1850.2.d.d	$1850$	$2$	1850.d	37.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2q^{7}-iq^{8}-3q^{9}+\cdots\)
1850.2.d.e	$1850$	$2$	1850.d	37.b	$2$	$4$	$4$	$14.772$	\(\Q(i, \sqrt{21})\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{3}q^{3}-q^{4}+(\beta _{1}+\beta _{2})q^{6}+\cdots\)
1850.2.d.f	$1850$	$2$	1850.d	37.b	$2$	$6$	$6$	$14.772$	6.0.399424.1	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-10\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(1+\beta _{1}+\beta _{3})q^{3}-q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
1850.2.d.g	$1850$	$2$	1850.d	37.b	$2$	$12$	$12$	$14.772$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{7}q^{3}-q^{4}-\beta _{1}q^{6}+(-1+\cdots)q^{7}+\cdots\)
1850.2.d.h	$1850$	$2$	1850.d	37.b	$2$	$12$	$12$	$14.772$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{7}q^{3}-q^{4}-\beta _{1}q^{6}+(1+\cdots)q^{7}+\cdots\)
1850.2.d.i	$1850$	$2$	1850.d	37.b	$2$	$20$	$20$	$14.772$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{2}q^{6}+\beta _{9}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 2}\)