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

• Label: 1275.4.cg
• Level: $1275$
• Weight: $4$
• Character orbit: 1275.cg
• Rep. character: $\chi_{1275}(19,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $4288$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1275.cg (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 425 \)
Character field:			\(\Q(\zeta_{40})\)
Sturm bound:			\(720\)

Dimensions

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

	Total	New	Old
Modular forms	8704	4288	4416
Cusp forms	8576	4288	4288
Eisenstein series	128	0	128

Trace form

4288 * q - 32 * q^5 - 80 * q^10 - 336 * q^11 + 16384 * q^16 + 1664 * q^20 + 16 * q^25 - 288 * q^26 + 1184 * q^29 - 1920 * q^33 - 992 * q^35 + 2024 * q^40 - 4224 * q^41 + 288 * q^45 + 2592 * q^46 - 384 * q^49 - 448 * q^50 - 1920 * q^53 + 6440 * q^58 - 2624 * q^61 + 9536 * q^65 - 6912 * q^69 - 3640 * q^70 + 5760 * q^73 - 6752 * q^74 - 96 * q^75 + 4480 * q^77 - 2592 * q^79 + 12832 * q^80 + 37520 * q^83 + 8064 * q^84 + 4560 * q^85 - 3080 * q^88 - 720 * q^90 + 576 * q^91 + 17200 * q^92 + 14288 * q^94 + 7120 * q^95 - 2016 * 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

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