Space of modular forms of level 675, weight 2, and Character 675.bg

• Label: 675.2.bg
• Level: $675$
• Weight: $2$
• Character orbit: 675.bg
• Rep. character: $\chi_{675}(4,\cdot)$
• Character field: $\Q(\zeta_{90})$
• Dimension: $2112$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.bg (of order \(90\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 675 \)
Character field:			\(\Q(\zeta_{90})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(675, [\chi])\).

	Total	New	Old
Modular forms	2208	2208	0
Cusp forms	2112	2112	0
Eisenstein series	96	96	0

Trace form

2112 * q - 30 * q^2 - 30 * q^3 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 15 * q^8 - 18 * q^9 - 12 * q^10 - 18 * q^11 - 30 * q^12 - 30 * q^13 - 18 * q^14 - 69 * q^15 - 6 * q^16 - 15 * q^17 - 9 * q^19 + 27 * q^20 - 54 * q^21 - 30 * q^22 - 30 * q^23 - 30 * q^24 + 12 * q^25 + 192 * q^26 - 30 * q^27 - 60 * q^28 - 18 * q^29 + 21 * q^30 - 30 * q^33 - 6 * q^34 - 3 * q^35 - 66 * q^36 - 15 * q^37 - 30 * q^38 - 48 * q^39 - 21 * q^40 - 18 * q^41 + 120 * q^42 - 69 * q^44 + 105 * q^45 - 9 * q^46 - 105 * q^47 - 180 * q^48 - 48 * q^49 - 114 * q^50 - 30 * q^51 - 90 * q^52 - 60 * q^53 - 54 * q^54 - 48 * q^55 - 105 * q^56 - 30 * q^58 - 9 * q^59 + 36 * q^60 - 18 * q^61 - 15 * q^62 - 30 * q^63 - 231 * q^64 - 75 * q^65 - 153 * q^66 + 60 * q^67 - 18 * q^69 - 102 * q^70 + 75 * q^71 - 30 * q^72 - 15 * q^73 - 78 * q^74 - 69 * q^75 - 72 * q^76 - 270 * q^77 - 315 * q^78 - 18 * q^79 - 90 * q^80 - 126 * q^81 - 30 * q^83 - 168 * q^84 - 9 * q^85 + 42 * q^86 - 180 * q^87 - 30 * q^88 - 111 * q^89 - 120 * q^90 - 9 * q^91 + 330 * q^92 - 18 * q^94 - 117 * q^95 + 30 * q^96 - 30 * q^97 - 15 * q^98 - 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(675, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
675.2.bg.a	$675$	$2$	675.bg	675.ag	$90$	$2112$	$88$	$5.390$		None		✓	✓	✓	675.2.bg.a	$4$	$0$	\(-30\)	\(-30\)	\(-36\)	\(0\)		$\mathrm{SU}(2)[C_{90}]$