Space of modular forms of level 2600, weight 2, and Character 2600.fm

• Label: 2600.2.fm
• Level: $2600$
• Weight: $2$
• Character orbit: 2600.fm
• Rep. character: $\chi_{2600}(37,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $6656$
• Sturm bound: $840$

Defining parameters

Level:	\( N \)	\(=\)	\( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2600.fm (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2600 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2600, [\chi])\).

	Total	New	Old
Modular forms	6784	6784	0
Cusp forms	6656	6656	0
Eisenstein series	128	128	0

Trace form

6656 * q - 14 * q^2 - 30 * q^4 - 12 * q^6 - 16 * q^7 - 20 * q^8 - 20 * q^9 - 20 * q^10 + 16 * q^12 - 40 * q^14 - 56 * q^15 - 6 * q^16 - 44 * q^17 - 12 * q^18 + 2 * q^20 - 6 * q^22 - 48 * q^23 + 24 * q^24 - 32 * q^26 + 6 * q^28 - 16 * q^30 - 24 * q^31 - 54 * q^32 - 28 * q^33 - 12 * q^34 - 18 * q^36 - 8 * q^38 - 40 * q^39 + 24 * q^40 - 24 * q^41 - 74 * q^42 - 20 * q^44 - 12 * q^46 - 24 * q^47 + 82 * q^48 - 3136 * q^49 - 140 * q^50 + 144 * q^52 + 138 * q^54 - 16 * q^55 - 88 * q^56 - 242 * q^58 + 32 * q^60 - 10 * q^62 + 148 * q^63 - 144 * q^65 - 24 * q^66 + 2 * q^68 + 142 * q^70 - 24 * q^71 - 16 * q^72 - 40 * q^73 - 16 * q^76 - 228 * q^78 - 80 * q^79 - 176 * q^80 - 780 * q^81 - 48 * q^82 + 34 * q^84 - 32 * q^86 - 40 * q^87 - 328 * q^88 - 140 * q^89 + 88 * q^90 - 48 * q^92 + 174 * q^94 - 48 * q^95 - 82 * q^96 - 28 * q^97 + 60 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2600, [\chi])\) into newform subspaces

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