Space of modular forms of level 615, weight 4, and Character 615.f

• Label: 615.4.f
• Level: $615$
• Weight: $4$
• Character orbit: 615.f
• Rep. character: $\chi_{615}(286,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $2$
• Sturm bound: $336$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 615 = 3 \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	615.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(336\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(615, [\chi])\).

	Total	New	Old
Modular forms	256	84	172
Cusp forms	248	84	164
Eisenstein series	8	0	8

Trace form

84 * q + 336 * q^4 - 756 * q^9 + 40 * q^10 + 1344 * q^16 - 208 * q^23 + 2100 * q^25 - 104 * q^31 - 960 * q^32 - 360 * q^33 - 3024 * q^36 + 680 * q^37 + 480 * q^40 + 1156 * q^41 + 1368 * q^42 + 232 * q^43 + 1864 * q^46 - 4844 * q^49 - 696 * q^51 + 456 * q^57 + 600 * q^59 - 544 * q^61 + 3824 * q^62 + 3744 * q^64 - 888 * q^66 + 144 * q^73 + 3432 * q^74 - 1824 * q^77 + 912 * q^78 - 1760 * q^80 + 6804 * q^81 + 6528 * q^82 + 3024 * q^83 + 3672 * q^84 + 136 * q^86 - 768 * q^87 - 360 * q^90 + 3984 * q^91 + 1832 * q^92 - 16392 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(615, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
615.4.f.a	$615$	$4$	615.f	41.b	$2$	$42$	$42$	$36.286$		None		✓			615.4.f.a	$2$	$0$	\(-4\)	\(0\)	\(-210\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
615.4.f.b	$615$	$4$	615.f	41.b	$2$	$42$	$42$	$36.286$		None		✓			615.4.f.b	$2$	$0$	\(4\)	\(0\)	\(210\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(615, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(615, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(123, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 2}\)