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

• Label: 2600.2.fb
• Level: $2600$
• Weight: $2$
• Character orbit: 2600.fb
• Rep. character: $\chi_{2600}(69,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $3328$
• Sturm bound: $840$

Defining parameters

Level:	\( N \)	\(=\)	\( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2600.fb (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2600 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(840\)

Dimensions

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

	Total	New	Old
Modular forms	3392	3392	0
Cusp forms	3328	3328	0
Eisenstein series	64	64	0

Trace form

3328 * q - 15 * q^2 - 3 * q^4 - 9 * q^6 + 402 * q^9 - 10 * q^10 - 20 * q^12 - 42 * q^15 + 9 * q^16 - 10 * q^17 - 30 * q^22 - 10 * q^23 - 42 * q^24 - 36 * q^25 + 8 * q^26 - 15 * q^28 - 5 * q^30 - 30 * q^33 - 13 * q^36 - 20 * q^38 - 24 * q^39 - 104 * q^40 - 30 * q^41 + 55 * q^42 + 51 * q^46 + 60 * q^48 - 1584 * q^49 + 75 * q^50 - 15 * q^52 - 87 * q^54 + 18 * q^55 - 6 * q^56 + 165 * q^58 - 55 * q^62 - 30 * q^63 - 60 * q^64 - 40 * q^66 - 18 * q^71 - 15 * q^72 - 54 * q^76 - 90 * q^78 - 104 * q^79 - 225 * q^80 + 390 * q^81 + 78 * q^84 - 10 * q^87 + 55 * q^88 - 18 * q^89 - 2 * q^90 - 200 * q^92 - 47 * q^94 - 78 * q^95 - 30 * q^97 + 90 * 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.