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Properties

Label 525.3.bn
Level $525$
Weight $3$
Character orbit 525.bn
Rep. character $\chi_{525}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $640$
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.bn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
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 640 672
Cusp forms 1248 640 608
Eisenstein series 64 0 64

Trace form

\( 640 q - 160 q^{4} + 6 q^{5} - 60 q^{8} + 240 q^{9} + O(q^{10}) \) \( 640 q - 160 q^{4} + 6 q^{5} - 60 q^{8} + 240 q^{9} - 78 q^{10} - 30 q^{11} - 60 q^{14} + 24 q^{15} + 320 q^{16} + 80 q^{22} + 140 q^{23} + 34 q^{25} - 120 q^{28} - 120 q^{29} + 180 q^{31} + 60 q^{35} + 960 q^{36} + 990 q^{38} - 330 q^{40} - 120 q^{42} - 160 q^{44} - 18 q^{45} - 20 q^{46} - 140 q^{49} + 180 q^{50} - 810 q^{52} - 100 q^{53} - 180 q^{56} + 60 q^{58} - 720 q^{59} - 162 q^{60} - 180 q^{61} + 90 q^{63} + 2060 q^{64} + 46 q^{65} - 720 q^{67} + 118 q^{70} - 160 q^{71} - 90 q^{72} - 480 q^{73} - 540 q^{74} - 144 q^{75} + 80 q^{79} - 1140 q^{80} + 720 q^{81} + 720 q^{84} + 1876 q^{85} + 240 q^{86} + 810 q^{88} + 430 q^{91} + 2340 q^{92} + 480 q^{94} - 318 q^{95} + 1350 q^{96} + 600 q^{98} - 120 q^{99} + O(q^{100}) \)

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.

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

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