Space of modular forms of level 2900, weight 2, and Character 2900.k

• Label: 2900.2.k
• Level: $2900$
• Weight: $2$
• Character orbit: 2900.k
• Rep. character: $\chi_{2900}(1351,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $558$
• Sturm bound: $900$

Defining parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 116 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(900\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2900, [\chi])\).

	Total	New	Old
Modular forms	924	582	342
Cusp forms	876	558	318
Eisenstein series	48	24	24

Trace form

558 * q + 6 * q^8 + 14 * q^12 + 12 * q^14 - 32 * q^16 + 14 * q^17 + 14 * q^18 - 16 * q^21 + 16 * q^24 + 6 * q^26 - 4 * q^29 + 10 * q^32 + 48 * q^36 + 10 * q^37 - 2 * q^41 + 30 * q^44 + 20 * q^46 - 50 * q^48 - 462 * q^49 + 32 * q^52 - 40 * q^53 + 16 * q^54 + 48 * q^56 - 52 * q^58 - 30 * q^61 - 30 * q^66 - 44 * q^68 + 32 * q^69 - 36 * q^72 - 30 * q^73 + 4 * q^74 - 4 * q^76 - 16 * q^77 + 40 * q^78 - 406 * q^81 + 24 * q^82 + 72 * q^84 + 124 * q^88 + 78 * q^89 + 28 * q^94 + 42 * q^97 - 4 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(580, [\chi])\)\(^{\oplus 2}\)