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Properties

Label 725.6.m
Level $725$
Weight $6$
Character orbit 725.m
Rep. character $\chi_{725}(144,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1488$
Sturm bound $450$

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Defining parameters

Level: \( N \) \(=\) \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 725.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 725 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(450\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(725, [\chi])\).

Total New Old
Modular forms 1504 1504 0
Cusp forms 1488 1488 0
Eisenstein series 16 16 0

Trace form

\( 1488 q - 5894 q^{4} + 8 q^{5} - 22 q^{6} - 29490 q^{9} + O(q^{10}) \) \( 1488 q - 5894 q^{4} + 8 q^{5} - 22 q^{6} - 29490 q^{9} - 10 q^{13} - 92038 q^{16} + 638 q^{20} - 10 q^{22} + 9210 q^{23} + 49600 q^{24} + 8496 q^{25} + 28470 q^{28} - 697 q^{29} + 29926 q^{30} + 7370 q^{33} + 30018 q^{34} + 26596 q^{35} - 446138 q^{36} + 86020 q^{38} - 9370 q^{42} - 30324 q^{45} - 3435800 q^{49} + 179400 q^{51} + 124600 q^{52} - 138590 q^{53} - 56296 q^{54} + 337370 q^{58} - 184806 q^{59} - 10 q^{62} + 168060 q^{63} - 1401334 q^{64} - 496142 q^{65} + 118350 q^{67} - 1816 q^{71} + 727652 q^{74} + 221100 q^{78} + 377462 q^{80} - 2265326 q^{81} - 10 q^{83} - 195248 q^{86} - 498740 q^{87} + 805310 q^{88} + 13028 q^{91} - 998670 q^{92} - 29562 q^{94} - 908408 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(725, [\chi])\) into newform subspaces

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