Space of modular forms of level 2475, weight 2, and Character 2475.dp

• Label: 2475.2.dp
• Level: $2475$
• Weight: $2$
• Character orbit: 2475.dp
• Rep. character: $\chi_{2475}(1063,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1184$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2475.dp (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2475, [\chi])\).

	Total	New	Old
Modular forms	2944	1216	1728
Cusp forms	2816	1184	1632
Eisenstein series	128	32	96

Trace form

1184 * q + 10 * q^2 - 10 * q^4 - 40 * q^7 + 10 * q^8 + 20 * q^10 + 6 * q^11 - 10 * q^13 + 10 * q^14 + 282 * q^16 + 20 * q^17 - 30 * q^19 - 6 * q^20 - 24 * q^22 + 2 * q^23 - 42 * q^25 + 12 * q^26 - 70 * q^28 + 10 * q^29 - 2 * q^31 - 30 * q^32 - 20 * q^34 + 10 * q^35 - 10 * q^37 + 4 * q^38 - 10 * q^40 + 10 * q^41 + 10 * q^44 - 10 * q^46 + 38 * q^47 + 50 * q^49 + 10 * q^50 - 10 * q^52 + 38 * q^53 - 50 * q^55 + 4 * q^56 - 34 * q^58 + 30 * q^59 + 50 * q^62 - 210 * q^64 - 50 * q^67 + 180 * q^68 - 40 * q^70 + 32 * q^71 + 20 * q^73 - 110 * q^74 + 124 * q^77 + 30 * q^79 - 118 * q^80 + 70 * q^82 + 110 * q^83 - 50 * q^85 + 2 * q^86 - 120 * q^88 + 20 * q^89 - 2 * q^91 + 38 * q^92 - 80 * q^94 - 70 * q^95 - 68 * q^97 + 80 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)