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

• Label: 1575.4.eb
• Level: $1575$
• Weight: $4$
• Character orbit: 1575.eb
• Rep. character: $\chi_{1575}(187,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $11456$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1575.eb (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1575 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(960\)

Dimensions

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

	Total	New	Old
Modular forms	11584	11584	0
Cusp forms	11456	11456	0
Eisenstein series	128	128	0

Trace form

11456 * q + 8 * q^2 - 24 * q^3 + 10 * q^4 - 8 * q^7 - 96 * q^8 - 10 * q^9 - 48 * q^10 - 12 * q^11 - 24 * q^12 - 10 * q^14 + 52 * q^15 - 22522 * q^16 - 192 * q^17 - 8 * q^18 - 60 * q^19 + 768 * q^20 - 12 * q^21 + 16 * q^22 - 224 * q^23 - 16 * q^25 - 96 * q^26 + 828 * q^27 - 176 * q^28 - 20 * q^29 - 1586 * q^30 - 18 * q^31 + 532 * q^32 + 936 * q^33 + 544 * q^35 - 280 * q^36 - 16 * q^37 + 2430 * q^39 - 526 * q^42 - 16 * q^43 - 20 * q^44 - 1392 * q^45 - 12 * q^46 - 24 * q^47 + 30 * q^48 + 1448 * q^50 - 16 * q^51 - 576 * q^53 - 30 * q^54 + 506 * q^56 - 2308 * q^57 - 960 * q^58 - 30 * q^59 + 3640 * q^60 - 18 * q^61 + 8174 * q^63 - 80 * q^64 + 704 * q^65 + 2574 * q^66 + 8 * q^67 + 9240 * q^69 + 992 * q^70 - 48 * q^71 + 1324 * q^72 - 48 * q^73 - 24 * q^75 + 768 * q^76 + 12512 * q^77 - 5390 * q^78 + 10 * q^79 - 432 * q^80 - 6 * q^81 - 672 * q^83 + 3820 * q^84 - 16 * q^85 - 12 * q^86 + 138 * q^87 + 2608 * q^88 - 20460 * q^89 - 23904 * q^90 - 24 * q^91 + 960 * q^92 + 5284 * q^93 - 30 * q^94 + 60 * q^95 - 18 * q^96 + 4300 * 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.