Space of modular forms of level 2535, weight 2, and Character 2535.k

• Label: 2535.2.k
• Level: $2535$
• Weight: $2$
• Character orbit: 2535.k
• Rep. character: $\chi_{2535}(1282,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $308$
• Sturm bound: $728$

Defining parameters

Level:	\( N \)	\(=\)	\( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2535.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2535, [\chi])\).

	Total	New	Old
Modular forms	784	308	476
Cusp forms	672	308	364
Eisenstein series	112	0	112

Trace form

308 * q - 308 * q^4 - 8 * q^5 + 8 * q^11 - 16 * q^12 - 4 * q^15 + 308 * q^16 + 28 * q^17 + 4 * q^18 - 8 * q^21 + 24 * q^22 - 16 * q^23 + 12 * q^25 + 16 * q^31 - 28 * q^34 - 32 * q^37 + 56 * q^40 - 4 * q^41 - 8 * q^43 - 40 * q^44 + 4 * q^45 + 16 * q^46 + 24 * q^47 + 32 * q^48 + 372 * q^49 + 32 * q^50 - 28 * q^53 + 8 * q^55 + 8 * q^58 - 32 * q^59 + 12 * q^60 - 72 * q^62 - 308 * q^64 - 16 * q^66 - 60 * q^68 - 16 * q^69 - 64 * q^70 - 40 * q^71 - 12 * q^72 + 32 * q^75 + 40 * q^76 + 48 * q^77 + 32 * q^80 - 308 * q^81 - 12 * q^82 + 104 * q^83 + 32 * q^84 + 4 * q^85 - 16 * q^86 + 24 * q^87 - 64 * q^88 + 36 * q^89 + 20 * q^90 + 64 * q^92 - 48 * q^95 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2535, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2535, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2535, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 2}\)