Space of modular forms of level 588, weight 2, and Character 588.b

• Label: 588.2.b
• Level: $588$
• Weight: $2$
• Character orbit: 588.b
• Rep. character: $\chi_{588}(391,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(588, [\chi])\).

	Total	New	Old
Modular forms	128	40	88
Cusp forms	96	40	56
Eisenstein series	32	0	32

Trace form

\( 40 q + 4 q^{2} - 4 q^{4} + 16 q^{8} + 40 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(588, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
588.2.b.a	$588$	$2$	588.b	28.d	$2$	$8$	$8$	$4.695$	8.0.562828176.1	None		$2$	$0$	\(-2\)	\(-8\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)
588.2.b.b	$588$	$2$	588.b	28.d	$2$	$8$	$8$	$4.695$	8.0.562828176.1	None		$2$	$0$	\(-2\)	\(8\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
588.2.b.c	$588$	$2$	588.b	28.d	$2$	$12$	$12$	$4.695$	12.0.\(\cdots\).1	None		$2$	$0$	\(4\)	\(-12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
588.2.b.d	$588$	$2$	588.b	28.d	$2$	$12$	$12$	$4.695$	12.0.\(\cdots\).1	None		$2$	$0$	\(4\)	\(12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(588, [\chi]) \cong \)