Space of modular forms of level 315, weight 2, and Character 315.l

• Label: 315.2.l
• Level: $315$
• Weight: $2$
• Character orbit: 315.l
• Rep. character: $\chi_{315}(121,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(315, [\chi])\).

	Total	New	Old
Modular forms	104	64	40
Cusp forms	88	64	24
Eisenstein series	16	0	16

Trace form

64 * q + 64 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 6 * q^9 + 2 * q^11 + 10 * q^12 + 2 * q^13 + 12 * q^14 - 2 * q^15 + 64 * q^16 - 16 * q^17 - 6 * q^18 - 4 * q^19 - 12 * q^20 - 22 * q^21 - 6 * q^23 - 32 * q^24 - 32 * q^25 - 8 * q^26 + 6 * q^27 - 8 * q^28 - 10 * q^29 + 2 * q^30 - 16 * q^31 - 40 * q^32 - 28 * q^33 - 60 * q^36 + 2 * q^37 - 44 * q^38 + 2 * q^39 + 10 * q^41 + 12 * q^42 + 8 * q^43 - 14 * q^44 + 6 * q^45 - 6 * q^46 + 104 * q^47 - 64 * q^48 + 4 * q^49 + 56 * q^51 + 8 * q^52 - 30 * q^54 - 42 * q^56 + 26 * q^57 + 20 * q^59 - 36 * q^60 - 16 * q^61 - 24 * q^62 + 44 * q^63 + 64 * q^64 - 4 * q^65 - 8 * q^66 - 28 * q^67 - 58 * q^68 - 24 * q^69 - 12 * q^70 + 48 * q^71 - 34 * q^72 - 28 * q^73 + 44 * q^74 - 16 * q^76 + 70 * q^77 + 40 * q^78 - 16 * q^79 - 28 * q^80 - 46 * q^81 - 68 * q^83 - 24 * q^84 + 6 * q^85 + 2 * q^86 + 26 * q^87 - 14 * q^89 + 18 * q^90 - 22 * q^91 - 100 * q^92 + 6 * q^93 - 24 * q^94 - 158 * q^96 + 2 * q^97 - 10 * q^98 - 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
315.2.l.a	$315$	$2$	315.l	63.h	$3$	$4$	$2$	$2.515$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		✓			315.2.k.a	$2$	$0$	\(-2\)	\(6\)	\(2\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(2-\beta _{3})q^{4}+\cdots\)
315.2.l.b	$315$	$2$	315.l	63.h	$3$	$24$	$12$	$2.515$		None		✓			315.2.k.b	$2$	$0$	\(2\)	\(-5\)	\(12\)	\(-11\)		$\mathrm{SU}(2)[C_{3}]$
315.2.l.c	$315$	$2$	315.l	63.h	$3$	$36$	$18$	$2.515$		None		✓	✓		315.2.k.c	$2$	$0$	\(0\)	\(-1\)	\(-18\)	\(-1\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)