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

• Label: 675.2.bd
• Level: $675$
• Weight: $2$
• Character orbit: 675.bd
• Rep. character: $\chi_{675}(8,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $448$
• 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.bd (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 225 \)
Character field:			\(\Q(\zeta_{60})\)
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	1536	512	1024
Cusp forms	1344	448	896
Eisenstein series	192	64	128

Trace form

448 * q + 24 * q^2 - 10 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 18 * q^11 - 8 * q^13 + 30 * q^14 - 50 * q^16 - 40 * q^19 + 48 * q^20 + 48 * q^23 + 16 * q^25 - 24 * q^28 + 30 * q^29 - 6 * q^31 + 60 * q^32 - 10 * q^34 - 44 * q^37 - 16 * q^40 + 18 * q^41 - 8 * q^43 - 24 * q^46 + 18 * q^47 - 24 * q^50 + 24 * q^52 - 24 * q^55 + 18 * q^56 - 4 * q^58 - 6 * q^61 - 40 * q^64 + 96 * q^65 - 14 * q^67 - 288 * q^68 - 28 * q^70 - 32 * q^73 - 32 * q^76 - 216 * q^77 - 10 * q^79 - 72 * q^82 - 36 * q^83 - 32 * q^85 + 18 * q^86 - 28 * q^88 - 24 * q^91 - 30 * q^92 - 130 * q^94 - 6 * q^95 - 38 * q^97

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.bd.a	$675$	$2$	675.bd	225.w	$60$	$448$	$28$	$5.390$		None			✓	✓	225.2.w.a	$4$	$0$	\(24\)	\(0\)	\(24\)	\(-8\)		$\mathrm{SU}(2)[C_{60}]$

Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(675, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)