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Properties

Label 1617.4.ci
Level $1617$
Weight $4$
Character orbit 1617.ci
Rep. character $\chi_{1617}(5,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $32064$
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.ci (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1617 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 32448 32448 0
Cusp forms 32064 32064 0
Eisenstein series 384 384 0

Trace form

\( 32064 q - 33 q^{3} + 2578 q^{4} - 42 q^{6} - 84 q^{7} - 39 q^{9} + O(q^{10}) \) \( 32064 q - 33 q^{3} + 2578 q^{4} - 42 q^{6} - 84 q^{7} - 39 q^{9} - 104 q^{10} - 136 q^{12} - 84 q^{13} + 78 q^{15} - 10542 q^{16} + 62 q^{18} - 108 q^{19} + 50 q^{21} + 1316 q^{22} + 513 q^{24} - 16630 q^{25} - 168 q^{27} - 280 q^{28} - 90 q^{30} + 1134 q^{31} + 1504 q^{33} - 224 q^{34} + 1006 q^{36} + 6 q^{37} - 125 q^{39} + 6090 q^{40} - 4922 q^{42} - 1504 q^{43} - 2224 q^{45} + 18 q^{46} + 4452 q^{49} - 351 q^{51} - 1782 q^{52} - 4588 q^{54} + 5558 q^{55} + 1024 q^{57} - 16342 q^{58} + 10221 q^{60} - 66 q^{61} - 3634 q^{63} - 79356 q^{64} - 4503 q^{66} + 1920 q^{67} + 10878 q^{69} - 5094 q^{70} + 1299 q^{72} - 2370 q^{73} + 3225 q^{75} + 1568 q^{76} + 19476 q^{78} + 888 q^{79} + 28605 q^{81} + 5238 q^{82} - 20249 q^{84} + 4972 q^{85} - 1182 q^{87} - 500 q^{88} + 1708 q^{90} + 32960 q^{91} - 1701 q^{93} + 1374 q^{94} + 6029 q^{96} + 35938 q^{99} + O(q^{100}) \)

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.