Properties

Label 2205.2.cq
Level $2205$
Weight $2$
Character orbit 2205.cq
Rep. character $\chi_{2205}(121,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $2688$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2205.cq (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2205, [\chi])\).

Total New Old
Modular forms 4080 2688 1392
Cusp forms 3984 2688 1296
Eisenstein series 96 0 96

Trace form

\( 2688q - 448q^{4} + 4q^{5} - 10q^{6} + 2q^{7} - 10q^{9} + O(q^{10}) \) \( 2688q - 448q^{4} + 4q^{5} - 10q^{6} + 2q^{7} - 10q^{9} + 130q^{12} - 2q^{13} + 58q^{14} - 448q^{16} + 16q^{17} + 6q^{18} + 4q^{19} + 12q^{20} + 22q^{21} - 78q^{23} + 32q^{24} + 224q^{25} + 8q^{26} + 78q^{27} + 8q^{28} - 78q^{29} - 2q^{30} + 16q^{31} + 40q^{32} + 28q^{33} + 10q^{36} + 26q^{37} + 44q^{38} - 12q^{39} - 10q^{41} - 96q^{42} - 8q^{43} + 22q^{44} - 6q^{45} - 78q^{46} - 20q^{47} + 64q^{48} - 4q^{49} - 26q^{51} + 104q^{52} + 8q^{53} + 30q^{54} - 238q^{56} - 10q^{57} - 20q^{59} - 70q^{60} - 82q^{61} + 24q^{62} - 44q^{63} - 448q^{64} + 190q^{66} + 28q^{67} - 278q^{68} - 144q^{69} + 12q^{70} - 32q^{71} + 6q^{72} + 28q^{73} - 16q^{74} + 16q^{76} - 70q^{77} + 244q^{78} + 4q^{79} - 168q^{80} - 110q^{81} + 68q^{83} + 332q^{84} + 14q^{86} - 138q^{87} + 14q^{89} - 18q^{90} + 22q^{91} - 236q^{92} - 30q^{93} + 24q^{94} - 206q^{96} - 2q^{97} - 102q^{98} - 58q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)