↑

Properties

Label 2205.2.dl
Level $2205$
Weight $2$
Character orbit 2205.dl
Rep. character $\chi_{2205}(236,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2688$
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.dl (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

\( 2688 q - 224 q^{4} + 14 q^{6} - 2 q^{7} - 26 q^{9} + O(q^{10}) \) \( 2688 q - 224 q^{4} + 14 q^{6} - 2 q^{7} - 26 q^{9} - 70 q^{12} + 6 q^{13} + 6 q^{14} + 224 q^{16} - 28 q^{18} + 24 q^{21} + 126 q^{23} + 18 q^{24} - 448 q^{25} + 24 q^{26} - 24 q^{27} + 8 q^{28} + 108 q^{29} + 4 q^{30} - 24 q^{31} + 24 q^{33} - 70 q^{36} - 26 q^{37} + 120 q^{38} + 24 q^{39} - 6 q^{41} + 168 q^{42} + 8 q^{43} + 66 q^{44} + 18 q^{45} + 78 q^{46} + 36 q^{47} - 60 q^{48} - 10 q^{49} - 46 q^{51} + 56 q^{52} - 24 q^{53} + 36 q^{54} - 102 q^{56} + 10 q^{57} - 30 q^{59} - 182 q^{60} - 136 q^{61} - 14 q^{63} + 448 q^{64} - 384 q^{66} - 14 q^{67} + 60 q^{68} - 168 q^{69} - 6 q^{70} + 48 q^{72} + 54 q^{77} - 176 q^{78} - 2 q^{79} + 246 q^{81} - 60 q^{83} - 254 q^{84} + 214 q^{87} + 42 q^{89} + 54 q^{90} + 6 q^{91} - 432 q^{92} + 36 q^{93} + 52 q^{96} + 6 q^{97} + 54 q^{98} + 134 q^{99} + O(q^{100}) \)

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

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