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Properties

Label 2205.4.db
Level $2205$
Weight $4$
Character orbit 2205.db
Rep. character $\chi_{2205}(4,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $12048$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.db (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2205 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2205, [\chi])\).

Total New Old
Modular forms 12144 12144 0
Cusp forms 12048 12048 0
Eisenstein series 96 96 0

Trace form

\( 12048 q - 4016 q^{4} - 5 q^{5} - 56 q^{6} + 156 q^{9} + O(q^{10}) \) \( 12048 q - 4016 q^{4} - 5 q^{5} - 56 q^{6} + 156 q^{9} - 42 q^{10} - 10 q^{11} - 24 q^{14} - 79 q^{15} + 15872 q^{16} - 24 q^{19} + 131 q^{20} - 398 q^{21} - 256 q^{24} - 5 q^{25} - 660 q^{26} + 326 q^{29} + 105 q^{30} + 12 q^{31} + 6 q^{34} - 307 q^{35} + 1156 q^{36} - 58 q^{39} - 479 q^{40} - 1528 q^{41} + 220 q^{44} - 545 q^{45} - 3360 q^{46} - 408 q^{49} + 84 q^{50} - 506 q^{51} + 1316 q^{54} + 1760 q^{55} - 2636 q^{56} + 2816 q^{59} + 180 q^{60} - 34 q^{61} + 125112 q^{64} - 650 q^{65} + 2382 q^{66} + 1582 q^{69} + 131 q^{70} + 4580 q^{71} + 446 q^{74} + 4519 q^{75} - 1066 q^{76} + 264 q^{79} - 2215 q^{80} + 12196 q^{81} - 6186 q^{84} + 120 q^{85} - 4622 q^{86} - 7402 q^{89} + 8723 q^{90} + 1324 q^{91} - 1176 q^{94} - 269 q^{95} - 8864 q^{96} + 10818 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

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