Space of modular forms of level 525, weight 8, and Character 525.m

• Label: 525.8.m
• Level: $525$
• Weight: $8$
• Character orbit: 525.m
• Rep. character: $\chi_{525}(118,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $336$
• Sturm bound: $640$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	525.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(525, [\chi])\).

	Total	New	Old
Modular forms	1144	336	808
Cusp forms	1096	336	760
Eisenstein series	48	0	48

Trace form

336 * q + 2136 * q^7 + 4008 * q^8 + 24224 * q^11 - 1121728 * q^16 + 27108 * q^21 - 111488 * q^22 + 351880 * q^23 - 402412 * q^28 + 513024 * q^32 - 15676416 * q^36 - 51824 * q^37 - 227988 * q^42 + 3842128 * q^43 + 1653704 * q^46 - 387936 * q^51 - 3568152 * q^53 + 18922464 * q^56 + 2414664 * q^57 - 2948536 * q^58 - 1557144 * q^63 - 13386336 * q^67 - 59511296 * q^71 + 2921832 * q^72 - 39532392 * q^77 + 1267704 * q^78 - 178564176 * q^81 - 18003896 * q^86 + 91841072 * q^88 + 38626892 * q^91 + 85842520 * q^92 - 12188232 * q^93 - 5145072 * q^98

Decomposition of \(S_{8}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(525, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)