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

• Label: 1275.4.cc
• Level: $1275$
• Weight: $4$
• Character orbit: 1275.cc
• Rep. character: $\chi_{1275}(106,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $2144$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1275.cc (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 425 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(720\)

Dimensions

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

	Total	New	Old
Modular forms	4352	2144	2208
Cusp forms	4288	2144	2144
Eisenstein series	64	0	64

Trace form

2144 * q + 2112 * q^4 + 32 * q^5 + 16 * q^7 - 40 * q^10 + 168 * q^11 - 96 * q^13 - 8192 * q^16 - 176 * q^17 - 576 * q^18 + 576 * q^20 - 336 * q^21 + 432 * q^22 + 336 * q^23 - 1120 * q^28 - 592 * q^29 - 2688 * q^30 + 576 * q^33 - 2256 * q^35 - 480 * q^37 - 704 * q^38 + 1204 * q^40 - 2112 * q^41 + 3388 * q^44 - 288 * q^45 + 1296 * q^46 + 1056 * q^48 + 1536 * q^52 - 3016 * q^55 + 2160 * q^57 + 3708 * q^58 + 1680 * q^61 - 216 * q^63 + 30720 * q^64 - 2952 * q^65 + 960 * q^67 + 6760 * q^68 + 960 * q^69 - 1472 * q^71 - 1728 * q^72 + 2112 * q^73 - 7688 * q^74 - 1200 * q^75 + 1344 * q^78 - 1296 * q^79 + 256 * q^80 + 43416 * q^81 - 4192 * q^82 + 4032 * q^84 - 2656 * q^85 + 2532 * q^88 + 3072 * q^89 - 360 * q^90 + 2088 * q^91 - 2920 * q^92 + 880 * q^95 - 1740 * q^96 + 6224 * q^97 + 14296 * q^98 - 1008 * 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

\( S_{4}^{\mathrm{old}}(1275, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 2}\)