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Properties

Label 456.3.x
Level $456$
Weight $3$
Character orbit 456.x
Rep. character $\chi_{456}(125,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $312$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 456.x (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 456 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(456, [\chi])\).

Total New Old
Modular forms 328 328 0
Cusp forms 312 312 0
Eisenstein series 16 16 0

Trace form

\( 312 q - 4 q^{4} + 7 q^{6} - 16 q^{7} - 2 q^{9} + O(q^{10}) \) \( 312 q - 4 q^{4} + 7 q^{6} - 16 q^{7} - 2 q^{9} + 4 q^{10} - 22 q^{12} + 34 q^{15} + 12 q^{16} - 26 q^{18} - 10 q^{22} - 37 q^{24} - 704 q^{25} - 34 q^{28} - 256 q^{30} - 144 q^{31} - 36 q^{33} + 12 q^{34} - 15 q^{36} - 44 q^{39} - 192 q^{40} + 50 q^{42} - 184 q^{46} - 11 q^{48} + 1800 q^{49} - 106 q^{52} + 6 q^{54} - 104 q^{55} - 62 q^{57} + 72 q^{58} - 94 q^{60} - 100 q^{63} + 464 q^{64} + 151 q^{66} + 112 q^{70} + 291 q^{72} + 76 q^{73} - 496 q^{76} + 192 q^{78} - 260 q^{79} + 54 q^{81} - 86 q^{82} - 196 q^{84} - 420 q^{87} - 1340 q^{88} + 460 q^{90} - 464 q^{94} + 470 q^{96} - 228 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(456, [\chi])\) into newform subspaces

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