Space of modular forms of level 1575, weight 2, and Character 1575.dk

• Label: 1575.2.dk
• Level: $1575$
• Weight: $2$
• Character orbit: 1575.dk
• Rep. character: $\chi_{1575}(109,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $784$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.dk (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

	Total	New	Old
Modular forms	1984	816	1168
Cusp forms	1856	784	1072
Eisenstein series	128	32	96

Trace form

784 * q + 5 * q^2 - 99 * q^4 + 5 * q^5 - 10 * q^8 - 5 * q^10 + 6 * q^11 - 20 * q^13 + 6 * q^14 + 85 * q^16 + 15 * q^17 - 11 * q^19 + 16 * q^20 + 20 * q^22 + 35 * q^23 + 9 * q^25 + 60 * q^26 - 60 * q^28 + 3 * q^31 + 44 * q^34 + 14 * q^35 - 5 * q^37 - 10 * q^38 - 33 * q^40 + 26 * q^41 + 31 * q^44 + 37 * q^46 + 5 * q^47 - 6 * q^49 + 86 * q^50 + 70 * q^52 + 35 * q^53 - 28 * q^55 - 32 * q^56 + 55 * q^58 + 15 * q^59 + 7 * q^61 - 100 * q^62 + 98 * q^64 + 43 * q^65 + 25 * q^67 + 5 * q^70 + 14 * q^71 - 45 * q^73 + 6 * q^74 + 132 * q^76 + 5 * q^77 + q^79 - 36 * q^80 - 10 * q^83 + 50 * q^85 - 35 * q^86 - 40 * q^88 + 42 * q^89 + 26 * q^91 - 190 * q^92 - 27 * q^94 + 25 * q^95 - 160 * q^97 - 180 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)