Space of modular forms of level 624, weight 2, and Character 624.bz

• Label: 624.2.bz
• Level: $624$
• Weight: $2$
• Character orbit: 624.bz
• Rep. character: $\chi_{624}(95,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $8$
• Sturm bound: $224$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bz (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 156 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(224\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(624, [\chi])\).

	Total	New	Old
Modular forms	248	56	192
Cusp forms	200	56	144
Eisenstein series	48	0	48

Trace form

\( 56 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(624, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
624.2.bz.a	$624$	$2$	624.bz	156.r	$6$	$2$	$1$	$4.983$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$1$	\(0\)	\(-3\)	\(0\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1-\zeta_{6})q^{3}-5\zeta_{6}q^{7}+3\zeta_{6}q^{9}+\cdots\)
624.2.bz.b	$624$	$2$	624.bz	156.r	$6$	$2$	$1$	$4.983$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(-1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{7}+3\zeta_{6}q^{9}+\cdots\)
624.2.bz.c	$624$	$2$	624.bz	156.r	$6$	$2$	$1$	$4.983$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(3\)	\(0\)	\(1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(1+\zeta_{6})q^{3}+\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(4+\cdots)q^{13}+\cdots\)
624.2.bz.d	$624$	$2$	624.bz	156.r	$6$	$2$	$1$	$4.983$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(3\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(1+\zeta_{6})q^{3}+5\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-4+\cdots)q^{13}+\cdots\)
624.2.bz.e	$624$	$2$	624.bz	156.r	$6$	$8$	$4$	$4.983$	8.0.3317760000.8	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(-\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots\)
624.2.bz.f	$624$	$2$	624.bz	156.r	$6$	$8$	$4$	$4.983$	8.0.\(\cdots\).2	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{4}-\beta _{6})q^{7}+\beta _{2}q^{9}+\cdots\)
624.2.bz.g	$624$	$2$	624.bz	156.r	$6$	$16$	$8$	$4.983$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(-6\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+(2+2\beta _{2}+2\beta _{3}-2\beta _{4}+2\beta _{7}+\cdots)q^{5}+\cdots\)
624.2.bz.h	$624$	$2$	624.bz	156.r	$6$	$16$	$8$	$4.983$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(3\)	\(0\)	\(6\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}+(2+2\beta _{2}+2\beta _{3}-2\beta _{4}+2\beta _{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(624, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)