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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

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

Display 100 coefficients 10 coefficients

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

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