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

• Label: 1850.2.b
• Level: $1850$
• Weight: $2$
• Character orbit: 1850.b
• Rep. character: $\chi_{1850}(149,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $16$
• Sturm bound: $570$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(570\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	298	54	244
Cusp forms	274	54	220
Eisenstein series	24	0	24

Trace form

\( 54 q - 54 q^{4} + 4 q^{6} - 78 q^{9} + O(q^{10}) \)

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.b.a	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{8}+\cdots\)
1850.2.b.b	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+2iq^{7}+\cdots\)
1850.2.b.c	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{7}+\cdots\)
1850.2.b.d	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+iq^{8}+3q^{9}-4q^{11}+\cdots\)
1850.2.b.e	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
1850.2.b.f	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-4iq^{7}+\cdots\)
1850.2.b.g	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)
1850.2.b.h	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
1850.2.b.i	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots\)
1850.2.b.j	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{6}-2\beta _{1}q^{7}+\cdots\)
1850.2.b.k	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+(1+\beta _{3})q^{6}+\cdots\)
1850.2.b.l	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
1850.2.b.m	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	\(\Q(i, \sqrt{33})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+2\beta _{2}q^{3}-q^{4}+2q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1850.2.b.n	$1850$	$2$	1850.b	5.b	$2$	$6$	$6$	$14.772$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(\beta _{3}-\beta _{5})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots\)
1850.2.b.o	$1850$	$2$	1850.b	5.b	$2$	$6$	$6$	$14.772$	6.0.3182656.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{5}q^{7}+\cdots\)
1850.2.b.p	$1850$	$2$	1850.b	5.b	$2$	$6$	$6$	$14.772$	6.0.37161216.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 2}\)