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Properties

Label 1500.4.r
Level $1500$
Weight $4$
Character orbit 1500.r
Rep. character $\chi_{1500}(299,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $2112$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1500.r (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1500, [\chi])\).

Total New Old
Modular forms 3680 2208 1472
Cusp forms 3520 2112 1408
Eisenstein series 160 96 64

Trace form

\( 2112 q + 6 q^{4} + 7 q^{6} + 6 q^{9} + O(q^{10}) \) \( 2112 q + 6 q^{4} + 7 q^{6} + 6 q^{9} + 5 q^{12} + 20 q^{13} - 126 q^{16} + 144 q^{21} + 10 q^{22} - 140 q^{24} + 650 q^{28} + 10 q^{33} - 42 q^{34} + 45 q^{36} - 1300 q^{37} + 1435 q^{42} + 434 q^{46} - 3050 q^{48} + 89816 q^{49} + 160 q^{52} - 1176 q^{54} + 3430 q^{58} + 588 q^{61} + 942 q^{64} + 3062 q^{66} + 426 q^{69} + 5 q^{72} + 20 q^{73} - 3264 q^{76} + 2935 q^{78} - 474 q^{81} - 5292 q^{84} - 1970 q^{88} + 8496 q^{94} + 2608 q^{96} - 9280 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1500, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1500, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1500, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)