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Properties

Label 1617.4.bt
Level $1617$
Weight $4$
Character orbit 1617.bt
Rep. character $\chi_{1617}(89,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $6720$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1617.bt (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1617, [\chi])\).

Total New Old
Modular forms 8112 6720 1392
Cusp forms 8016 6720 1296
Eisenstein series 96 0 96

Trace form

\( 6720 q - 2240 q^{4} - 56 q^{6} - 92 q^{7} + 224 q^{9} + O(q^{10}) \) \( 6720 q - 2240 q^{4} - 56 q^{6} - 92 q^{7} + 224 q^{9} + 440 q^{12} + 168 q^{15} + 8960 q^{16} + 70 q^{18} + 612 q^{19} + 572 q^{21} + 288 q^{24} + 14000 q^{25} - 1600 q^{28} - 448 q^{30} - 1020 q^{31} + 1008 q^{34} - 980 q^{36} - 2492 q^{37} + 420 q^{39} + 1332 q^{40} + 1440 q^{42} - 1288 q^{43} + 3348 q^{45} + 13524 q^{46} - 772 q^{49} - 1288 q^{51} + 12080 q^{52} - 3810 q^{54} - 3360 q^{57} - 1176 q^{58} + 1344 q^{60} - 3028 q^{61} + 204 q^{63} + 71680 q^{64} - 2200 q^{66} + 196 q^{67} - 15816 q^{70} - 560 q^{72} - 3492 q^{73} + 9108 q^{75} - 17136 q^{76} + 1302 q^{78} + 1036 q^{79} + 17248 q^{81} - 7392 q^{82} + 8248 q^{84} - 3696 q^{85} - 3636 q^{87} + 35756 q^{90} - 1572 q^{91} + 20888 q^{93} - 288 q^{94} + 50062 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1617, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1617, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1617, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)