↑

Properties

Label 2205.2.k
Level $2205$
Weight $2$
Character orbit 2205.k
Rep. character $\chi_{2205}(961,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $320$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2205.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 704 320 384
Cusp forms 640 320 320
Eisenstein series 64 0 64

Trace form

\( 320 q - 160 q^{4} - 8 q^{5} + 4 q^{6} + 2 q^{9} + O(q^{10}) \) \( 320 q - 160 q^{4} - 8 q^{5} + 4 q^{6} + 2 q^{9} + 8 q^{11} + 20 q^{12} - 2 q^{13} + 4 q^{15} - 160 q^{16} + 16 q^{17} + 12 q^{18} + 4 q^{19} + 12 q^{20} - 12 q^{23} + 14 q^{24} + 320 q^{25} + 8 q^{26} - 6 q^{27} + 14 q^{29} + 4 q^{30} - 8 q^{31} - 20 q^{32} + 4 q^{33} + 68 q^{36} - 2 q^{37} - 88 q^{38} + 32 q^{39} - 10 q^{41} - 8 q^{43} + 6 q^{44} - 6 q^{45} + 6 q^{46} + 52 q^{47} + 64 q^{48} + 58 q^{51} + 16 q^{52} - 8 q^{53} - 120 q^{54} - 42 q^{57} + 10 q^{59} - 46 q^{60} - 8 q^{61} + 24 q^{62} + 320 q^{64} - 4 q^{65} - 16 q^{66} - 14 q^{67} - 116 q^{68} + 24 q^{69} - 64 q^{71} + 56 q^{72} + 28 q^{73} + 144 q^{74} + 16 q^{76} - 44 q^{78} - 14 q^{79} + 28 q^{80} - 66 q^{81} + 68 q^{83} - 12 q^{85} + 36 q^{86} + 22 q^{87} + 14 q^{89} - 18 q^{90} + 156 q^{92} + 12 q^{93} - 12 q^{94} - 64 q^{96} - 2 q^{97} + 14 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)