Space of modular forms of level 1550, weight 2, and Character 1550.b

• Label: 1550.2.b
• Level: $1550$
• Weight: $2$
• Character orbit: 1550.b
• Rep. character: $\chi_{1550}(249,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $11$
• Sturm bound: $480$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1550 = 2 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1550.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(480\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1550, [\chi])\).

	Total	New	Old
Modular forms	252	44	208
Cusp forms	228	44	184
Eisenstein series	24	0	24

Trace form

\( 44 q - 44 q^{4} + 8 q^{6} - 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1550, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1550.2.b.a	$1550$	$2$	1550.b	5.b	$2$	$2$	$2$	$12.377$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-4iq^{7}+\cdots\)
1550.2.b.b	$1550$	$2$	1550.b	5.b	$2$	$2$	$2$	$12.377$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}+2q^{9}+\cdots\)
1550.2.b.c	$1550$	$2$	1550.b	5.b	$2$	$2$	$2$	$12.377$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}-iq^{8}+3q^{9}-2iq^{13}+\cdots\)
1550.2.b.d	$1550$	$2$	1550.b	5.b	$2$	$2$	$2$	$12.377$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}-5iq^{7}+iq^{8}+3q^{9}+\cdots\)
1550.2.b.e	$1550$	$2$	1550.b	5.b	$2$	$2$	$2$	$12.377$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
1550.2.b.f	$1550$	$2$	1550.b	5.b	$2$	$4$	$4$	$12.377$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
1550.2.b.g	$1550$	$2$	1550.b	5.b	$2$	$4$	$4$	$12.377$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{2}q^{3}-q^{4}-\beta _{3}q^{6}-2\beta _{1}q^{7}+\cdots\)
1550.2.b.h	$1550$	$2$	1550.b	5.b	$2$	$4$	$4$	$12.377$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
1550.2.b.i	$1550$	$2$	1550.b	5.b	$2$	$6$	$6$	$12.377$	6.0.5089536.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{4})q^{3}-q^{4}+(1+\cdots)q^{6}+\cdots\)
1550.2.b.j	$1550$	$2$	1550.b	5.b	$2$	$6$	$6$	$12.377$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(\beta _{1}+\beta _{3})q^{3}-q^{4}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
1550.2.b.k	$1550$	$2$	1550.b	5.b	$2$	$10$	$10$	$12.377$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}-q^{4}+\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1550, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1550, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)