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Properties

Label 1617.2.bc
Level $1617$
Weight $2$
Character orbit 1617.bc
Rep. character $\chi_{1617}(188,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1128$
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.bc (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 1368 1128 240
Cusp forms 1320 1128 192
Eisenstein series 48 0 48

Trace form

\( 1128 q + 192 q^{4} - 28 q^{6} + 8 q^{7} - 20 q^{9} + O(q^{10}) \) \( 1128 q + 192 q^{4} - 28 q^{6} + 8 q^{7} - 20 q^{9} + 70 q^{12} + 12 q^{15} - 200 q^{16} + 20 q^{18} + 10 q^{21} - 196 q^{25} - 12 q^{28} + 16 q^{30} + 112 q^{34} + 80 q^{36} - 88 q^{37} - 24 q^{39} + 112 q^{40} + 84 q^{42} + 48 q^{43} - 160 q^{46} - 4 q^{49} + 16 q^{51} - 252 q^{52} + 30 q^{57} + 12 q^{58} - 48 q^{60} - 196 q^{61} - 6 q^{63} + 216 q^{64} + 70 q^{66} - 32 q^{67} + 120 q^{70} - 40 q^{72} - 252 q^{75} - 336 q^{76} + 126 q^{78} - 56 q^{79} + 140 q^{81} + 140 q^{82} - 268 q^{84} - 104 q^{85} - 350 q^{90} - 8 q^{91} - 50 q^{93} + 14 q^{96} + O(q^{100}) \)

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

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