Space of modular forms of level 1725, weight 2, and Character 1725.bf

• Label: 1725.2.bf
• Level: $1725$
• Weight: $2$
• Character orbit: 1725.bf
• Rep. character: $\chi_{1725}(49,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $720$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 1725 = 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1725.bf (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(\zeta_{22})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1725, [\chi])\).

	Total	New	Old
Modular forms	2520	720	1800
Cusp forms	2280	720	1560
Eisenstein series	240	0	240

Trace form

720 * q + 64 * q^4 + 8 * q^6 + 72 * q^9 + 8 * q^11 - 16 * q^14 - 48 * q^16 - 8 * q^19 - 8 * q^21 - 24 * q^24 - 24 * q^26 + 8 * q^29 + 40 * q^31 + 60 * q^34 - 64 * q^36 + 72 * q^39 + 56 * q^41 - 124 * q^44 - 16 * q^46 + 8 * q^49 + 16 * q^51 + 36 * q^54 - 48 * q^56 + 80 * q^59 - 56 * q^61 + 216 * q^64 - 20 * q^69 + 8 * q^71 - 56 * q^74 + 92 * q^76 + 96 * q^79 - 72 * q^81 + 56 * q^84 + 352 * q^86 - 96 * q^89 + 344 * q^91 - 56 * q^94 - 112 * q^96 - 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1725, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1725, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1725, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)