Space of modular forms of level 185, weight 2, and Character 185.k

• Label: 185.2.k
• Level: $185$
• Weight: $2$
• Character orbit: 185.k
• Rep. character: $\chi_{185}(68,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $34$
• Newform subspaces: $4$
• Sturm bound: $38$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(38\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(185, [\chi])\).

	Total	New	Old
Modular forms	42	42	0
Cusp forms	34	34	0
Eisenstein series	8	8	0

Trace form

\( 34 q - 2 q^{2} - 4 q^{3} + 30 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(185, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
185.2.k.a	$185$	$2$	185.k	185.k	$4$	$2$	$1$	$1.477$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(-2\)	\(-4\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}+(-2+2i)q^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
185.2.k.b	$185$	$2$	185.k	185.k	$4$	$2$	$1$	$1.477$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(2\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}+(1-i)q^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
185.2.k.c	$185$	$2$	185.k	185.k	$4$	$6$	$3$	$1.477$	6.0.350464.1	None		$2$	$0$	\(-2\)	\(2\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
185.2.k.d	$185$	$2$	185.k	185.k	$4$	$24$	$12$	$1.477$		None		$2$	$0$	\(4\)	\(-4\)	\(8\)	\(6\)		$\mathrm{SU}(2)[C_{4}]$