Space of modular forms of level 592, weight 2, and Character 592.be

• Label: 592.2.be
• Level: $592$
• Weight: $2$
• Character orbit: 592.be
• Rep. character: $\chi_{592}(319,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $76$
• Newform subspaces: $6$
• Sturm bound: $152$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.be (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 148 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(152\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(592, [\chi])\).

	Total	New	Old
Modular forms	328	76	252
Cusp forms	280	76	204
Eisenstein series	48	0	48

Trace form

\( 76 q - 12 q^{5} - 38 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(592, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
592.2.be.a	$592$	$2$	592.be	148.l	$12$	$4$	$1$	$4.727$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(1+\zeta_{12}+2\zeta_{12}^{2}-3\zeta_{12}^{3})q^{5}+\cdots\)
592.2.be.b	$592$	$2$	592.be	148.l	$12$	$8$	$2$	$4.727$	8.0.1234538496.2	None		$2$	$0$	\(0\)	\(-4\)	\(2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+2\beta _{3}+\beta _{4}-\beta _{6})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
592.2.be.c	$592$	$2$	592.be	148.l	$12$	$8$	$2$	$4.727$	8.0.1234538496.2	None		$2$	$0$	\(0\)	\(4\)	\(2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{3}+2\beta _{4}-\beta _{6})q^{3}+(-1-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
592.2.be.d	$592$	$2$	592.be	148.l	$12$	$16$	$4$	$4.727$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{9}q^{3}+(-1+\beta _{8})q^{5}+(\beta _{3}+\beta _{14}+\cdots)q^{7}+\cdots\)
592.2.be.e	$592$	$2$	592.be	148.l	$12$	$20$	$5$	$4.727$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(-6\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{10}+\beta _{13})q^{3}+(-1+\beta _{2}-\beta _{7}+\cdots)q^{5}+\cdots\)
592.2.be.f	$592$	$2$	592.be	148.l	$12$	$20$	$5$	$4.727$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(-4\)	\(6\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{10}-\beta _{13})q^{3}+(-1+\beta _{2}-\beta _{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(592, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(592, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 2}\)