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

• Label: 2475.2.fs
• Level: $2475$
• Weight: $2$
• Character orbit: 2475.fs
• Rep. character: $\chi_{2475}(7,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $3392$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2475.fs (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 495 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(720\)

Dimensions

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

	Total	New	Old
Modular forms	5952	3520	2432
Cusp forms	5568	3392	2176
Eisenstein series	384	128	256

Trace form

3392 * q + 10 * q^2 + 14 * q^3 - 40 * q^6 + 10 * q^7 + 40 * q^8 - 8 * q^11 + 44 * q^12 + 10 * q^13 - 412 * q^16 + 40 * q^17 + 20 * q^18 + 32 * q^23 + 80 * q^26 - 4 * q^27 + 40 * q^28 - 12 * q^31 + 74 * q^33 + 168 * q^36 + 12 * q^37 - 38 * q^38 - 20 * q^41 - 76 * q^42 - 80 * q^46 - 2 * q^47 + 144 * q^48 + 120 * q^51 + 10 * q^52 - 96 * q^53 + 144 * q^56 + 100 * q^57 - 14 * q^58 - 20 * q^61 + 340 * q^62 + 20 * q^63 - 172 * q^66 + 40 * q^67 + 50 * q^68 + 40 * q^71 + 170 * q^72 + 40 * q^73 - 100 * q^77 - 24 * q^78 + 36 * q^81 + 8 * q^82 + 10 * q^83 + 24 * q^86 + 100 * q^88 + 96 * q^91 + 154 * q^92 - 2 * q^93 - 960 * q^96 + 12 * q^97

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

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)