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Properties

Label 2205.4.cz
Level $2205$
Weight $4$
Character orbit 2205.cz
Rep. character $\chi_{2205}(164,\cdot)$
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.cz (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

\( 12048 q - 8010 q^{4} - 18 q^{5} + 48 q^{6} + 44 q^{9} + O(q^{10}) \) \( 12048 q - 8010 q^{4} - 18 q^{5} + 48 q^{6} + 44 q^{9} - 22 q^{10} - 36 q^{11} + 96 q^{14} + 5 q^{15} - 31722 q^{16} - 72 q^{19} + 3 q^{20} - 70 q^{21} + 524 q^{24} - 8 q^{25} + 48 q^{26} - 156 q^{29} - 218 q^{30} + 34 q^{34} + 765 q^{35} + 1076 q^{36} + 168 q^{39} + 419 q^{40} - 660 q^{41} + 816 q^{44} - 2283 q^{45} + 3256 q^{46} - 210 q^{49} + 300 q^{50} + 1258 q^{51} - 2200 q^{54} + 2114 q^{55} + 3654 q^{56} - 30 q^{59} + 731 q^{60} - 14 q^{61} - 124680 q^{64} - 21 q^{65} + 1806 q^{66} + 1658 q^{69} - 970 q^{70} + 19404 q^{71} + 60 q^{74} - 6827 q^{75} - 1326 q^{76} + 480 q^{79} - 3855 q^{80} - 6312 q^{81} + 710 q^{84} + 120 q^{85} + 4122 q^{86} + 26706 q^{89} + 7234 q^{90} - 1420 q^{91} - 14 q^{94} - 21 q^{95} - 4706 q^{96} - 10914 q^{99} + O(q^{100}) \)

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.