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

• Label: 1275.4.ce
• Level: $1275$
• Weight: $4$
• Character orbit: 1275.ce
• Rep. character: $\chi_{1275}(2,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $8576$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1275.ce (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1275 \)
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	8704	0
Cusp forms	8576	8576	0
Eisenstein series	128	128	0

Trace form

8576 * q - 16 * q^3 - 8512 * q^4 - 12 * q^6 - 32 * q^7 - 20 * q^9 + 32 * q^10 + 124 * q^12 + 96 * q^13 - 184 * q^15 - 33584 * q^16 - 32 * q^18 - 40 * q^19 + 320 * q^22 + 280 * q^24 - 656 * q^25 - 520 * q^27 - 320 * q^28 + 64 * q^30 - 24 * q^31 - 32 * q^33 + 88 * q^34 + 660 * q^36 - 6800 * q^37 - 20 * q^39 + 1544 * q^40 - 1004 * q^42 + 896 * q^45 - 24 * q^46 + 11020 * q^48 - 32 * q^51 + 2496 * q^52 + 44 * q^54 - 912 * q^55 + 1596 * q^57 + 4256 * q^58 - 2988 * q^60 + 2856 * q^61 - 9496 * q^63 - 130432 * q^64 + 12288 * q^66 + 32 * q^67 - 40 * q^69 - 5728 * q^70 + 280 * q^72 - 16400 * q^73 - 124 * q^75 + 960 * q^76 + 1496 * q^78 + 4280 * q^79 + 2720 * q^82 - 40 * q^84 + 8224 * q^85 + 8180 * q^87 + 8096 * q^88 + 8452 * q^90 + 7896 * q^91 + 88 * q^94 + 408 * q^96 + 2080 * q^97

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

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