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

• Label: 2535.2.i
• Level: $2535$
• Weight: $2$
• Character orbit: 2535.i
• Rep. character: $\chi_{2535}(991,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $204$
• Sturm bound: $728$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	784	204	580
Cusp forms	672	204	468
Eisenstein series	112	0	112

Trace form

204 * q - 2 * q^3 - 100 * q^4 + 2 * q^7 - 102 * q^9 - 4 * q^10 + 8 * q^11 + 8 * q^12 + 8 * q^14 - 88 * q^16 - 12 * q^17 + 8 * q^20 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 24 * q^24 + 204 * q^25 + 4 * q^27 + 36 * q^28 - 16 * q^29 - 4 * q^30 + 12 * q^31 - 20 * q^32 - 16 * q^34 + 4 * q^35 - 100 * q^36 - 8 * q^37 - 64 * q^38 + 24 * q^40 - 32 * q^41 + 4 * q^42 - 2 * q^43 + 8 * q^44 - 8 * q^46 + 48 * q^47 + 8 * q^48 - 96 * q^49 + 112 * q^53 - 20 * q^55 - 16 * q^56 + 48 * q^57 + 8 * q^58 + 16 * q^59 - 46 * q^61 - 44 * q^62 + 2 * q^63 + 288 * q^64 - 40 * q^66 - 6 * q^67 - 120 * q^68 - 8 * q^69 - 16 * q^70 - 8 * q^71 - 52 * q^73 - 68 * q^74 - 2 * q^75 + 8 * q^76 + 104 * q^77 + 12 * q^79 + 32 * q^80 - 102 * q^81 - 40 * q^82 + 8 * q^83 + 12 * q^84 + 48 * q^86 - 40 * q^87 - 40 * q^88 + 48 * q^89 + 8 * q^90 - 56 * q^92 + 6 * q^93 + 40 * q^94 + 8 * q^95 + 56 * q^96 + 26 * q^97 + 72 * q^98 - 16 * 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

\( S_{2}^{\mathrm{old}}(2535, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 2}\)