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

• Label: 1575.4.dw
• Level: $1575$
• Weight: $4$
• Character orbit: 1575.dw
• Rep. character: $\chi_{1575}(131,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $5728$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1575.dw (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1575 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(960\)

Dimensions

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

	Total	New	Old
Modular forms	5792	5792	0
Cusp forms	5728	5728	0
Eisenstein series	64	64	0

Trace form

5728 * q - 9 * q^3 + 5690 * q^4 - 12 * q^5 - 48 * q^6 - 8 * q^7 - 3 * q^9 - 24 * q^10 - 9 * q^11 - 57 * q^12 - 9 * q^14 - 299 * q^15 - 22566 * q^16 + 144 * q^17 - 56 * q^18 - 18 * q^19 - 24 * q^20 - 111 * q^21 - 38 * q^22 + 303 * q^23 + 198 * q^24 + 4 * q^25 - 48 * q^26 - 828 * q^27 - 220 * q^28 - 18 * q^29 + 302 * q^30 - 9 * q^33 - 48 * q^34 + 1110 * q^35 - 190 * q^36 - 6 * q^37 - 9 * q^38 + 1547 * q^39 - 435 * q^40 - 922 * q^42 - 16 * q^43 + 720 * q^44 - 2796 * q^45 - 38 * q^46 - 18 * q^47 + 618 * q^48 - 8 * q^49 + 1440 * q^50 - 1292 * q^51 + 759 * q^52 - 57 * q^54 + 3030 * q^56 - 2988 * q^57 - 533 * q^58 - 18 * q^59 - 4660 * q^60 - 8952 * q^62 - 6926 * q^63 + 88344 * q^64 - 171 * q^66 - 6 * q^67 + 9192 * q^68 - 2610 * q^69 - 3150 * q^70 - 5883 * q^72 - 18 * q^73 - 120 * q^74 + 8898 * q^75 + 288 * q^76 - 4905 * q^77 + 6772 * q^78 + 498 * q^79 - 15996 * q^80 + 209 * q^81 - 96 * q^82 + 3564 * q^84 - 133 * q^85 - 8349 * q^86 - 3645 * q^87 + 1251 * q^88 + 6120 * q^89 + 25812 * q^90 - 2070 * q^91 + 5550 * q^92 + 2312 * q^93 - 1833 * q^96 + 72 * q^98 - 306 * q^99

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

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