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

• Label: 2475.2.cd
• Level: $2475$
• Weight: $2$
• Character orbit: 2475.cd
• Rep. character: $\chi_{2475}(289,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $592$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2475.cd (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(720\)

Dimensions

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

	Total	New	Old
Modular forms	1472	608	864
Cusp forms	1408	592	816
Eisenstein series	64	16	48

Trace form

592 * q + 5 * q^2 + 145 * q^4 + q^5 + 5 * q^7 + 5 * q^8 - 4 * q^10 + 6 * q^11 + 9 * q^14 - 155 * q^16 + 9 * q^19 + 17 * q^20 - 10 * q^22 + 10 * q^23 + 15 * q^25 - q^26 + 45 * q^28 - 11 * q^29 + 6 * q^31 - 4 * q^34 + 43 * q^35 - 40 * q^37 + 35 * q^38 + 7 * q^40 + 20 * q^41 + 21 * q^44 - q^46 + 135 * q^49 + 30 * q^50 - 5 * q^52 - 10 * q^53 - 8 * q^55 + q^56 + 30 * q^58 + q^59 + 54 * q^61 - 90 * q^62 + 195 * q^64 + 10 * q^65 + 25 * q^67 - 85 * q^68 - 27 * q^70 + 4 * q^71 - 20 * q^73 - 27 * q^74 + 114 * q^76 - 40 * q^77 + 15 * q^79 + 9 * q^80 - 80 * q^82 + 55 * q^83 - 20 * q^85 - 15 * q^86 - 50 * q^88 - 4 * q^89 - 30 * q^91 + 42 * q^94 + 34 * q^95 - 5 * q^97 - 40 * 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

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