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

• Label: 1275.4.by
• Level: $1275$
• Weight: $4$
• Character orbit: 1275.by
• Rep. character: $\chi_{1275}(137,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $3840$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1275.by (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 75 \)
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	3840	512
Cusp forms	4288	3840	448
Eisenstein series	64	0	64

Trace form

3840 * q - 8 * q^3 - 24 * q^7 - 192 * q^10 + 128 * q^12 + 48 * q^13 + 16 * q^15 + 15360 * q^16 - 444 * q^18 - 120 * q^19 - 768 * q^22 + 2304 * q^25 + 592 * q^27 + 1152 * q^28 + 580 * q^30 - 584 * q^33 - 288 * q^37 - 4880 * q^39 - 2856 * q^40 + 656 * q^42 - 552 * q^43 + 3712 * q^45 - 764 * q^48 + 1224 * q^52 + 168 * q^55 + 1648 * q^57 + 384 * q^58 + 1712 * q^60 - 3872 * q^63 + 5760 * q^64 + 2496 * q^67 - 7176 * q^70 - 17556 * q^72 - 2952 * q^73 - 15672 * q^75 - 10092 * q^78 + 1280 * q^81 - 6600 * q^82 - 2504 * q^87 + 13200 * q^88 - 3392 * q^90 + 9376 * q^93 + 38640 * q^94 + 25440 * 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.

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

\( S_{4}^{\mathrm{old}}(1275, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)