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

• Label: 588.2.e
• Level: $588$
• Weight: $2$
• Character orbit: 588.e
• Rep. character: $\chi_{588}(491,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $6$
• Sturm bound: $224$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(224\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	128	92	36
Cusp forms	96	72	24
Eisenstein series	32	20	12

Trace form

\( 72 q + 4 q^{4} + 6 q^{6} + 4 q^{9} + O(q^{10}) \)

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.e.a	$588$	$2$	588.e	12.b	$2$	$4$	$4$	$4.695$	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-21}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+\beta _{3}q^{6}+\cdots\)
588.2.e.b	$588$	$2$	588.e	12.b	$2$	$8$	$8$	$4.695$	8.0.3317760000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}-\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
588.2.e.c	$588$	$2$	588.e	12.b	$2$	$12$	$12$	$4.695$	12.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{10}q^{3}+(-\beta _{3}+\beta _{5})q^{4}+\cdots\)
588.2.e.d	$588$	$2$	588.e	12.b	$2$	$12$	$12$	$4.695$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
588.2.e.e	$588$	$2$	588.e	12.b	$2$	$12$	$12$	$4.695$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots\)
588.2.e.f	$588$	$2$	588.e	12.b	$2$	$24$	$24$	$4.695$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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