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Properties

Label 525.3.y
Level $525$
Weight $3$
Character orbit 525.y
Rep. character $\chi_{525}(34,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $320$
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.y (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 656 320 336
Cusp forms 624 320 304
Eisenstein series 32 0 32

Trace form

\( 320 q + 160 q^{4} + 60 q^{8} - 240 q^{9} + O(q^{10}) \) \( 320 q + 160 q^{4} + 60 q^{8} - 240 q^{9} - 60 q^{11} + 60 q^{14} - 24 q^{15} - 320 q^{16} + 40 q^{22} + 340 q^{23} - 16 q^{25} + 120 q^{28} - 60 q^{29} - 288 q^{30} + 114 q^{35} + 480 q^{36} + 120 q^{42} - 320 q^{44} + 320 q^{46} + 140 q^{49} - 84 q^{50} + 100 q^{53} + 180 q^{56} - 60 q^{58} - 432 q^{60} - 90 q^{63} + 220 q^{64} + 296 q^{65} - 1440 q^{67} - 424 q^{70} - 80 q^{71} - 180 q^{72} - 120 q^{74} - 200 q^{79} - 720 q^{81} + 360 q^{84} + 92 q^{85} + 480 q^{86} + 3600 q^{88} + 110 q^{91} - 2340 q^{92} + 684 q^{95} - 180 q^{98} + 120 q^{99} + O(q^{100}) \)

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

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