Space of modular forms of level 525, weight 6, and Character 525.t

• Label: 525.6.t
• Level: $525$
• Weight: $6$
• Character orbit: 525.t
• Rep. character: $\chi_{525}(26,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $494$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(525, [\chi])\).

	Total	New	Old
Modular forms	824	518	306
Cusp forms	776	494	282
Eisenstein series	48	24	24

Trace form

494 * q + 3 * q^3 + 3842 * q^4 + 169 * q^7 + 81 * q^9 + 1734 * q^12 - 59598 * q^16 - 1300 * q^18 - 723 * q^19 - 2544 * q^21 - 180 * q^22 - 6642 * q^24 - 58 * q^28 - 1989 * q^31 - 1050 * q^33 - 29004 * q^36 + 8201 * q^37 + 2265 * q^39 - 25200 * q^42 - 7930 * q^43 - 19376 * q^46 - 857 * q^49 - 13134 * q^51 + 112716 * q^52 - 117072 * q^54 - 48918 * q^57 + 63630 * q^58 + 69342 * q^61 - 73565 * q^63 - 1827828 * q^64 - 122094 * q^66 - 126239 * q^67 + 109990 * q^72 - 36513 * q^73 + 168360 * q^78 + 9353 * q^79 + 32793 * q^81 + 73800 * q^82 - 390042 * q^84 - 336450 * q^87 - 68190 * q^88 - 139733 * q^91 + 33225 * q^93 - 632328 * q^94 - 245484 * q^96 + 210612 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(525, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)