Space of modular forms of level 310, weight 2, and Character 310.e

• Label: 310.2.e
• Level: $310$
• Weight: $2$
• Character orbit: 310.e
• Rep. character: $\chi_{310}(191,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	310.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(310, [\chi])\).

	Total	New	Old
Modular forms	104	24	80
Cusp forms	88	24	64
Eisenstein series	16	0	16

Trace form

24 * q + 24 * q^4 - 4 * q^7 - 16 * q^9 - 4 * q^11 + 20 * q^13 - 4 * q^14 + 24 * q^16 + 12 * q^17 + 16 * q^18 + 8 * q^19 - 20 * q^21 - 8 * q^23 - 12 * q^25 - 12 * q^26 + 24 * q^27 - 4 * q^28 - 8 * q^29 - 8 * q^30 - 20 * q^31 + 8 * q^33 - 4 * q^34 - 16 * q^35 - 16 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^39 - 4 * q^41 + 24 * q^43 - 4 * q^44 + 8 * q^45 + 8 * q^46 - 8 * q^47 - 20 * q^49 + 48 * q^51 + 20 * q^52 - 48 * q^54 - 4 * q^55 - 4 * q^56 - 4 * q^57 - 16 * q^58 + 8 * q^59 + 24 * q^61 + 12 * q^62 - 24 * q^63 + 24 * q^64 + 8 * q^65 + 24 * q^66 - 4 * q^67 + 12 * q^68 + 4 * q^69 - 8 * q^71 + 16 * q^72 - 4 * q^73 + 4 * q^74 + 8 * q^76 - 104 * q^77 - 32 * q^78 - 20 * q^79 - 60 * q^81 - 16 * q^82 - 20 * q^84 - 16 * q^86 - 40 * q^87 - 72 * q^89 - 8 * q^90 - 8 * q^91 - 8 * q^92 + 48 * q^93 - 32 * q^94 - 16 * q^95 - 24 * q^97 + 24 * q^98 - 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(310, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
310.2.e.a	$310$	$2$	310.e	31.c	$3$	$6$	$3$	$2.475$	6.0.309123.1	None		✓			310.2.e.a	$2$	$0$	\(-6\)	\(-1\)	\(-3\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{2}q^{6}+\cdots\)
310.2.e.b	$310$	$2$	310.e	31.c	$3$	$6$	$3$	$2.475$	6.0.49572675.1	None		✓			310.2.e.b	$2$	$0$	\(-6\)	\(1\)	\(3\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
310.2.e.c	$310$	$2$	310.e	31.c	$3$	$6$	$3$	$2.475$	6.0.309123.1	None		✓			310.2.e.c	$2$	$0$	\(6\)	\(-1\)	\(3\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(\beta _{1}-\beta _{5})q^{3}+q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
310.2.e.d	$310$	$2$	310.e	31.c	$3$	$6$	$3$	$2.475$	6.0.771147.1	None		✓			310.2.e.d	$2$	$0$	\(6\)	\(1\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+\beta _{4}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(310, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(310, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)