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Properties

Label 525.3.bi
Level $525$
Weight $3$
Character orbit 525.bi
Rep. character $\chi_{525}(22,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $480$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.bi (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(525, [\chi])\).

Total New Old
Modular forms 1312 480 832
Cusp forms 1248 480 768
Eisenstein series 64 0 64

Trace form

\( 480 q - 8 q^{2} - 16 q^{5} + 48 q^{8} + O(q^{10}) \) \( 480 q - 8 q^{2} - 16 q^{5} + 48 q^{8} + 40 q^{10} + 48 q^{12} - 64 q^{13} + 480 q^{16} - 24 q^{17} + 96 q^{18} + 200 q^{19} + 488 q^{20} + 72 q^{22} + 32 q^{23} + 136 q^{25} + 80 q^{26} - 200 q^{29} - 336 q^{30} - 1176 q^{32} - 288 q^{33} - 200 q^{34} - 720 q^{36} + 232 q^{37} - 56 q^{38} + 1568 q^{40} - 320 q^{41} + 112 q^{43} + 1400 q^{44} + 72 q^{45} + 256 q^{47} - 192 q^{48} + 256 q^{50} - 96 q^{52} - 8 q^{53} - 880 q^{55} - 48 q^{57} - 2008 q^{58} + 192 q^{60} + 480 q^{61} - 1824 q^{62} + 1600 q^{64} - 632 q^{65} + 752 q^{67} - 568 q^{68} - 112 q^{70} - 144 q^{72} - 144 q^{73} - 144 q^{75} - 112 q^{77} + 216 q^{78} - 400 q^{79} + 528 q^{80} + 1080 q^{81} + 1008 q^{82} + 32 q^{83} - 64 q^{85} + 1536 q^{87} - 1136 q^{88} + 3000 q^{89} + 24 q^{90} + 1496 q^{92} + 720 q^{93} + 400 q^{94} + 264 q^{95} - 120 q^{96} + 816 q^{97} + 56 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)