Space of modular forms of level 875, weight 2, and Character 875.bb

• Label: 875.2.bb
• Level: $875$
• Weight: $2$
• Character orbit: 875.bb
• Rep. character: $\chi_{875}(82,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $864$
• Newform subspaces: $3$
• Sturm bound: $200$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(200\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(875, [\chi])\).

	Total	New	Old
Modular forms	1760	1056	704
Cusp forms	1440	864	576
Eisenstein series	320	192	128

Trace form

864 * q + 8 * q^2 + 24 * q^3 + 10 * q^4 + 10 * q^7 + 36 * q^8 + 10 * q^9 - 18 * q^11 + 36 * q^12 + 20 * q^14 - 90 * q^16 + 42 * q^17 + 14 * q^18 + 30 * q^19 - 36 * q^21 - 32 * q^22 + 40 * q^23 - 144 * q^26 - 22 * q^28 - 54 * q^31 - 8 * q^32 + 30 * q^33 + 120 * q^36 + 10 * q^37 - 72 * q^38 - 30 * q^39 - 6 * q^42 + 108 * q^43 + 10 * q^44 - 18 * q^46 + 54 * q^47 - 48 * q^51 - 216 * q^52 - 50 * q^53 + 30 * q^54 + 12 * q^56 + 216 * q^57 + 4 * q^58 - 90 * q^59 - 54 * q^61 + 66 * q^63 + 100 * q^64 - 270 * q^66 - 4 * q^67 - 342 * q^68 - 72 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 + 10 * q^79 - 30 * q^81 - 216 * q^82 - 20 * q^84 - 18 * q^86 + 48 * q^87 + 122 * q^88 - 120 * q^89 - 36 * q^91 + 4 * q^92 - 106 * q^93 + 30 * q^94 - 270 * q^96 - 222 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(875, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
875.2.bb.a	$875$	$2$	875.bb	175.x	$60$	$288$	$18$	$6.987$		None					175.2.x.a	$4$	$0$	\(-2\)	\(-6\)	\(0\)	\(10\)		$\mathrm{SU}(2)[C_{60}]$
875.2.bb.b	$875$	$2$	875.bb	175.x	$60$	$288$	$18$	$6.987$		None					175.2.x.a	$4$	$0$	\(2\)	\(6\)	\(0\)	\(-10\)		$\mathrm{SU}(2)[C_{60}]$
875.2.bb.c	$875$	$2$	875.bb	175.x	$60$	$288$	$18$	$6.987$		None					175.2.x.a	$4$	$0$	\(8\)	\(24\)	\(0\)	\(10\)		$\mathrm{SU}(2)[C_{60}]$

Decomposition of \(S_{2}^{\mathrm{old}}(875, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(875, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)