Space of modular forms of level 616, weight 2, and Character 616.bi

• Label: 616.2.bi
• Level: $616$
• Weight: $2$
• Character orbit: 616.bi
• Rep. character: $\chi_{616}(13,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $368$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bi (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 616 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(616, [\chi])\).

	Total	New	Old
Modular forms	400	400	0
Cusp forms	368	368	0
Eisenstein series	32	32	0

Trace form

\( 368 q - 10 q^{2} - 4 q^{4} - 10 q^{7} - 10 q^{8} - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(616, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
616.2.bi.a	$616$	$2$	616.bi	616.ai	$10$	$8$	$2$	$4.919$	8.0.37515625.1	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
616.2.bi.b	$616$	$2$	616.bi	616.ai	$10$	$8$	$2$	$4.919$	8.0.37515625.1	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
616.2.bi.c	$616$	$2$	616.bi	616.ai	$10$	$352$	$88$	$4.919$		None		$8$	$0$	\(-10\)	\(0\)	\(0\)	\(-10\)		$\mathrm{SU}(2)[C_{10}]$