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Properties

Label 1617.2.bt
Level $1617$
Weight $2$
Character orbit 1617.bt
Rep. character $\chi_{1617}(89,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2232$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1617.bt (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1617, [\chi])\).

Total New Old
Modular forms 2736 2232 504
Cusp forms 2640 2232 408
Eisenstein series 96 0 96

Trace form

\( 2232 q - 184 q^{4} + 28 q^{6} + 6 q^{7} + 32 q^{9} + O(q^{10}) \) \( 2232 q - 184 q^{4} + 28 q^{6} + 6 q^{7} + 32 q^{9} - 40 q^{12} - 12 q^{15} + 180 q^{16} + 10 q^{18} - 6 q^{19} + 2 q^{21} - 36 q^{24} + 182 q^{25} + 40 q^{28} + 8 q^{30} + 54 q^{31} - 112 q^{34} - 80 q^{36} + 12 q^{37} - 12 q^{39} - 172 q^{40} - 48 q^{42} - 20 q^{43} + 54 q^{45} - 332 q^{46} - 22 q^{49} + 8 q^{51} - 68 q^{52} - 66 q^{54} - 30 q^{57} - 36 q^{58} - 24 q^{60} + 134 q^{61} + 24 q^{63} + 344 q^{64} - 40 q^{66} - 2 q^{67} - 24 q^{70} - 20 q^{72} + 6 q^{73} + 180 q^{75} + 336 q^{76} - 126 q^{78} - 14 q^{79} - 224 q^{81} - 56 q^{82} + 160 q^{84} + 104 q^{85} - 18 q^{87} - 448 q^{90} - 46 q^{91} - 424 q^{93} - 48 q^{94} - 710 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1617, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1617, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1617, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)