↑

Properties

Label 2205.4.cc
Level $2205$
Weight $4$
Character orbit 2205.cc
Rep. character $\chi_{2205}(97,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2848$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2205.cc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2205, [\chi])\).

Total New Old
Modular forms 4096 2912 1184
Cusp forms 3968 2848 1120
Eisenstein series 128 64 64

Trace form

\( 2848 q + 4 q^{2} + 32 q^{8} + O(q^{10}) \) \( 2848 q + 4 q^{2} + 32 q^{8} - 8 q^{11} - 184 q^{15} + 22024 q^{16} - 24 q^{18} - 72 q^{22} + 212 q^{23} + 4 q^{25} + 996 q^{30} + 796 q^{32} + 2848 q^{36} + 16 q^{37} - 8 q^{43} - 1984 q^{46} + 2024 q^{50} - 512 q^{51} - 2224 q^{53} + 568 q^{57} - 940 q^{58} + 1304 q^{60} + 1396 q^{65} + 4 q^{67} + 4608 q^{71} - 1520 q^{72} - 1772 q^{78} - 7624 q^{81} - 8 q^{85} + 1744 q^{86} + 2628 q^{88} + 3032 q^{92} + 3456 q^{93} - 100 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2205, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

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