Space of modular forms of level 285, weight 4, and Character 285.x

• Label: 285.4.x
• Level: $285$
• Weight: $4$
• Character orbit: 285.x
• Rep. character: $\chi_{285}(88,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $240$
• Sturm bound: $160$

Defining parameters

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	285.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(285, [\chi])\).

	Total	New	Old
Modular forms	496	240	256
Cusp forms	464	240	224
Eisenstein series	32	0	32

Trace form

240 * q - 16 * q^5 + 12 * q^6 + 16 * q^7 + 112 * q^11 + 1884 * q^16 - 128 * q^17 + 1520 * q^20 + 288 * q^21 + 432 * q^22 + 64 * q^23 - 296 * q^25 - 1216 * q^26 - 764 * q^28 - 96 * q^30 - 3036 * q^32 + 576 * q^33 + 1256 * q^35 - 4428 * q^36 + 432 * q^38 + 2172 * q^40 - 2664 * q^41 + 1200 * q^43 - 1584 * q^47 - 2232 * q^51 + 1872 * q^53 + 448 * q^55 + 1008 * q^57 - 6760 * q^58 + 1152 * q^60 + 960 * q^61 - 2108 * q^62 + 72 * q^63 - 2736 * q^66 - 2640 * q^67 + 7064 * q^68 - 3024 * q^70 + 2268 * q^72 - 1920 * q^73 - 6328 * q^76 + 6640 * q^77 + 1800 * q^78 + 2184 * q^80 + 9720 * q^81 + 4308 * q^82 + 7136 * q^83 + 1000 * q^85 - 1056 * q^86 - 3648 * q^87 + 324 * q^90 - 5184 * q^91 - 7356 * q^92 + 2736 * q^93 - 9432 * q^95 - 13416 * q^96 - 4896 * q^97 - 7872 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(285, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(285, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(285, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)