Space of modular forms of level 1575, weight 4, and Character 1575.cs

• Label: 1575.4.cs
• Level: $1575$
• Weight: $4$
• Character orbit: 1575.cs
• Rep. character: $\chi_{1575}(46,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $2384$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1575.cs (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{15})\)
Sturm bound:			\(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1575, [\chi])\).

	Total	New	Old
Modular forms	5824	2416	3408
Cusp forms	5696	2384	3312
Eisenstein series	128	32	96

Trace form

2384 * q + 3 * q^2 + 1181 * q^4 - 32 * q^7 - 82 * q^8 - 35 * q^10 - 39 * q^11 - 12 * q^13 - 84 * q^14 + 4685 * q^16 + 243 * q^17 + 149 * q^19 + 636 * q^20 - 140 * q^22 + 59 * q^23 + 174 * q^25 + 1240 * q^26 + 1060 * q^28 + 60 * q^29 + 783 * q^31 - 884 * q^32 - 876 * q^34 + 114 * q^35 + 45 * q^37 - 888 * q^38 + 367 * q^40 + 1036 * q^41 - 8 * q^43 + 691 * q^44 - 263 * q^46 + 427 * q^47 + 644 * q^49 - 6654 * q^50 + 1514 * q^52 - 757 * q^53 - 1878 * q^55 + 3558 * q^56 + 1073 * q^58 - 1905 * q^59 + 1057 * q^61 - 5932 * q^62 - 31802 * q^64 - 147 * q^65 + 83 * q^67 - 6346 * q^68 + 1375 * q^70 - 3496 * q^71 + 1677 * q^73 - 1454 * q^74 + 12452 * q^76 + 3509 * q^77 - 419 * q^79 - 6056 * q^80 - 2488 * q^82 + 7864 * q^83 - 3190 * q^85 + 2975 * q^86 + 1456 * q^88 - 93 * q^89 + 876 * q^91 + 6506 * q^92 + 1373 * q^94 - 570 * q^95 + 8976 * q^97 + 5144 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)