Space of modular forms of level 1275, weight 4, and Character 1275.bb

• Label: 1275.4.bb
• Level: $1275$
• Weight: $4$
• Character orbit: 1275.bb
• Rep. character: $\chi_{1275}(32,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $1280$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1275.bb (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 255 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1275, [\chi])\).

	Total	New	Old
Modular forms	2208	1312	896
Cusp forms	2112	1280	832
Eisenstein series	96	32	64

Trace form

1280 * q + 4 * q^3 + 5056 * q^4 - 8 * q^6 + 8 * q^7 + 144 * q^12 + 96 * q^13 + 19680 * q^16 + 8 * q^18 + 96 * q^19 + 360 * q^22 - 280 * q^24 + 820 * q^27 - 280 * q^28 - 880 * q^31 + 8 * q^33 - 128 * q^34 - 520 * q^36 + 1160 * q^37 + 1472 * q^39 - 984 * q^42 + 2288 * q^46 - 1180 * q^48 + 1536 * q^49 + 1880 * q^51 + 2576 * q^52 - 64 * q^54 + 1616 * q^57 + 4296 * q^58 + 3632 * q^61 - 2616 * q^63 + 68448 * q^64 - 8 * q^66 + 112 * q^67 + 280 * q^72 - 1480 * q^73 - 272 * q^76 + 1516 * q^78 + 5568 * q^79 + 5640 * q^82 + 8136 * q^88 + 4016 * q^91 + 4144 * q^94 - 2248 * q^96 + 2120 * q^97 + 2328 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1275, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1275, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1275, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)