Space of modular forms of level 60, weight 8, and Character 60.d

• Label: 60.8.d
• Level: $60$
• Weight: $8$
• Character orbit: 60.d
• Rep. character: $\chi_{60}(49,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	60.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(60, [\chi])\).

	Total	New	Old
Modular forms	90	6	84
Cusp forms	78	6	72
Eisenstein series	12	0	12

Trace form

6 * q + 170 * q^5 - 4374 * q^9 + 4696 * q^11 + 3780 * q^15 + 39360 * q^19 - 9936 * q^21 - 107850 * q^25 + 464844 * q^29 + 57864 * q^31 - 399680 * q^35 + 524880 * q^39 - 729740 * q^41 - 123930 * q^45 + 2964954 * q^49 - 579096 * q^51 - 4003080 * q^55 + 4827064 * q^59 - 4085508 * q^61 - 2929800 * q^65 + 1710504 * q^69 + 58560 * q^71 - 707400 * q^75 - 6930792 * q^79 + 3188646 * q^81 + 7866120 * q^85 - 7994980 * q^89 - 7680 * q^91 + 6139200 * q^95 - 3423384 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(60, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
60.8.d.a	$60$	$8$	60.d	5.b	$2$	$2$	$2$	$18.743$	\(\Q(\sqrt{-1}) \)	None		✓			60.8.d.a	$2$	$0$	\(0\)	\(0\)	\(500\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-27 i q^{3}+(125 i+250)q^{5}+722 i q^{7}+\cdots\)
60.8.d.b	$60$	$8$	60.d	5.b	$2$	$4$	$4$	$18.743$	\(\Q(i, \sqrt{1129})\)	None		✓	✓		60.8.d.b	$2$	$0$	\(0\)	\(0\)	\(-330\)	\(0\)	$2\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3^{3}\beta _{1}q^{3}+(-82-3^{3}\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(60, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(60, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)