Properties

Label 2205.2.de
Level $2205$
Weight $2$
Character orbit 2205.de
Rep. character $\chi_{2205}(41,\cdot)$
Character field $\Q(\zeta_{42})$
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.de (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
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

\( 2688 q - 224 q^{4} - 28 q^{6} - 2 q^{7} + 10 q^{9} + O(q^{10}) \) \( 2688 q - 224 q^{4} - 28 q^{6} - 2 q^{7} + 10 q^{9} - 70 q^{12} + 186 q^{14} + 224 q^{16} - 4 q^{18} - 18 q^{21} - 90 q^{23} + 224 q^{25} - 42 q^{27} - 16 q^{28} - 90 q^{29} + 4 q^{30} + 140 q^{36} - 20 q^{37} + 24 q^{39} - 18 q^{42} - 16 q^{43} + 60 q^{46} + 252 q^{47} + 8 q^{49} - 64 q^{51} + 56 q^{52} - 20 q^{57} + 70 q^{60} + 98 q^{61} + 52 q^{63} + 448 q^{64} - 42 q^{66} + 28 q^{67} + 336 q^{69} - 6 q^{70} - 84 q^{72} - 72 q^{74} + 54 q^{77} - 68 q^{78} + 4 q^{79} - 30 q^{81} - 320 q^{84} + 108 q^{86} + 112 q^{87} - 12 q^{91} + 444 q^{92} + 36 q^{93} + 490 q^{96} - 268 q^{99} + O(q^{100}) \)

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

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