Space of modular forms of level 855, weight 4, and Character 855.dh

• Label: 855.4.dh
• Level: $855$
• Weight: $4$
• Character orbit: 855.dh
• Rep. character: $\chi_{855}(47,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $4272$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	855.dh (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 855 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(855, [\chi])\).

	Total	New	Old
Modular forms	4368	4368	0
Cusp forms	4272	4272	0
Eisenstein series	96	96	0

Trace form

4272 * q - 18 * q^2 - 12 * q^3 - 18 * q^5 - 24 * q^6 + 6 * q^7 - 24 * q^10 - 6 * q^12 - 6 * q^13 + 492 * q^15 - 12 * q^16 + 432 * q^17 + 24 * q^18 - 36 * q^20 - 24 * q^21 + 186 * q^22 - 954 * q^23 - 6 * q^25 - 2448 * q^26 - 6 * q^27 + 360 * q^28 - 6 * q^30 - 24 * q^31 - 18 * q^32 - 300 * q^33 - 24 * q^36 - 48 * q^37 - 18 * q^38 - 6 * q^40 - 36 * q^41 + 1284 * q^42 - 6 * q^43 - 2742 * q^45 - 24 * q^46 - 18 * q^47 + 2526 * q^48 + 3312 * q^51 - 102 * q^52 + 726 * q^55 - 72 * q^56 + 180 * q^57 - 12 * q^58 + 3156 * q^60 - 12 * q^61 - 144 * q^62 - 5454 * q^63 + 7992 * q^66 - 6 * q^67 - 18 * q^68 - 6 * q^70 + 14100 * q^72 - 24 * q^73 + 9888 * q^75 - 12 * q^76 - 36 * q^77 + 8418 * q^78 + 11088 * q^80 - 2952 * q^81 - 24 * q^82 - 18 * q^83 - 6 * q^85 - 24984 * q^86 - 1830 * q^87 + 6150 * q^88 + 9516 * q^90 - 48 * q^91 + 126 * q^92 - 7332 * q^93 - 18 * q^95 - 26976 * q^96 - 6 * q^97 + 7074 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(855, [\chi])\) into newform subspaces

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