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Properties

Label 525.3.bq
Level $525$
Weight $3$
Character orbit 525.bq
Rep. character $\chi_{525}(44,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1248$
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.bq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(240\)

Dimensions

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

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

Trace form

\( 1248 q - 5 q^{3} + 298 q^{4} - 28 q^{6} - 3 q^{9} + O(q^{10}) \) \( 1248 q - 5 q^{3} + 298 q^{4} - 28 q^{6} - 3 q^{9} - 32 q^{10} - 5 q^{12} - 40 q^{13} - 104 q^{15} + 586 q^{16} - 6 q^{19} - 63 q^{21} - 120 q^{22} + 26 q^{24} - 4 q^{25} + 400 q^{27} - 300 q^{28} - 25 q^{30} - 66 q^{31} + 20 q^{33} - 216 q^{34} - 352 q^{36} - 10 q^{37} + 49 q^{39} - 184 q^{40} + 350 q^{42} - 45 q^{45} - 18 q^{46} - 60 q^{48} + 8 q^{49} - 164 q^{51} + 610 q^{52} + 5 q^{54} + 460 q^{55} + 50 q^{58} - 465 q^{60} - 6 q^{61} - 530 q^{63} - 1912 q^{64} - 269 q^{66} - 10 q^{67} - 258 q^{69} + 500 q^{70} - 165 q^{72} - 170 q^{73} - 211 q^{75} + 256 q^{76} - 110 q^{78} - 286 q^{79} - 283 q^{81} + 231 q^{84} + 664 q^{85} - 5 q^{87} + 170 q^{88} - 6 q^{90} + 326 q^{91} - 198 q^{94} + 355 q^{96} + 240 q^{97} + 132 q^{99} + O(q^{100}) \)

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.