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Properties

Label 600.3.bb
Level $600$
Weight $3$
Character orbit 600.bb
Rep. character $\chi_{600}(91,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $480$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 600.bb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(600, [\chi])\).

Total New Old
Modular forms 976 480 496
Cusp forms 944 480 464
Eisenstein series 32 0 32

Trace form

\( 480 q + 18 q^{8} - 360 q^{9} + O(q^{10}) \) \( 480 q + 18 q^{8} - 360 q^{9} - 22 q^{10} + 24 q^{12} - 60 q^{14} - 60 q^{16} + 16 q^{17} - 32 q^{20} - 146 q^{22} + 24 q^{25} + 100 q^{26} + 124 q^{28} - 60 q^{30} + 140 q^{32} + 80 q^{34} - 96 q^{35} - 170 q^{38} + 320 q^{40} - 80 q^{41} - 60 q^{42} + 128 q^{43} + 210 q^{44} - 100 q^{46} - 144 q^{48} - 3360 q^{49} - 352 q^{50} - 56 q^{52} + 180 q^{56} + 238 q^{58} + 126 q^{60} + 138 q^{62} - 150 q^{64} + 104 q^{65} + 120 q^{66} - 864 q^{67} + 352 q^{68} + 156 q^{70} + 54 q^{72} - 240 q^{73} + 220 q^{74} - 192 q^{75} - 360 q^{76} + 216 q^{78} + 16 q^{80} - 1080 q^{81} + 768 q^{82} - 320 q^{83} + 360 q^{84} + 300 q^{86} + 982 q^{88} - 600 q^{89} + 204 q^{90} + 1462 q^{92} - 350 q^{94} - 480 q^{96} + 192 q^{97} - 628 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)