Space of modular forms of level 612, weight 2, and Character 612.b

• Label: 612.2.b
• Level: $612$
• Weight: $2$
• Character orbit: 612.b
• Rep. character: $\chi_{612}(577,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $216$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 612 = 2^{2} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	612.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(216\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(612, [\chi])\).

	Total	New	Old
Modular forms	120	8	112
Cusp forms	96	8	88
Eisenstein series	24	0	24

Trace form

\( 8 q + 2 q^{17} - 12 q^{19} - 4 q^{25} - 20 q^{35} - 4 q^{43} + 20 q^{47} + 12 q^{49} + 24 q^{53} + 12 q^{55} + 16 q^{67} + 24 q^{77} - 28 q^{83} - 16 q^{85} - 20 q^{89}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(612, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
612.2.b.a	$612$	$2$	612.b	17.b	$2$	$2$	$2$	$4.887$	\(\Q(\sqrt{-2}) \)	None					68.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+3\beta q^{7}-\beta q^{11}-4q^{13}+\cdots\)
612.2.b.b	$612$	$2$	612.b	17.b	$2$	$2$	$2$	$4.887$	\(\Q(\sqrt{-1}) \)	None					204.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}-2 i q^{7}+3 i q^{11}+3 q^{13}+\cdots\)
612.2.b.c	$612$	$2$	612.b	17.b	$2$	$4$	$4$	$4.887$	\(\Q(i, \sqrt{17})\)	\(\Q(\sqrt{-51}) \)		✓	✓		612.2.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{5}+(\beta _{1}+2\beta _{2})q^{11}+(1-\beta _{3})q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(612, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(612, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 2}\)