↑

Properties

Label 2205.2.be
Level $2205$
Weight $2$
Character orbit 2205.be
Rep. character $\chi_{2205}(1256,\cdot)$
Character field $\Q(\zeta_{6})$
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.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 320 q + 160 q^{4} + 6 q^{9} + O(q^{10}) \) \( 320 q + 160 q^{4} + 6 q^{9} + 6 q^{13} + 4 q^{15} - 160 q^{16} - 28 q^{18} + 18 q^{24} + 320 q^{25} + 24 q^{26} + 18 q^{27} - 18 q^{29} + 4 q^{30} - 24 q^{31} + 24 q^{33} - 44 q^{36} + 2 q^{37} + 120 q^{38} + 48 q^{39} - 6 q^{41} + 8 q^{43} + 18 q^{44} + 18 q^{45} - 6 q^{46} + 36 q^{47} - 60 q^{48} - 38 q^{51} - 72 q^{53} + 36 q^{54} - 22 q^{57} - 30 q^{59} + 46 q^{60} + 60 q^{61} - 320 q^{64} - 12 q^{65} - 48 q^{66} - 14 q^{67} + 60 q^{68} + 104 q^{72} + 84 q^{78} + 10 q^{79} - 82 q^{81} - 60 q^{83} + 12 q^{85} + 102 q^{87} + 42 q^{89} + 54 q^{90} - 12 q^{92} + 84 q^{93} - 60 q^{96} + 6 q^{97} + 94 q^{99} + O(q^{100}) \)

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

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