↑

Properties

Label 1600.3.ca
Level $1600$
Weight $3$
Character orbit 1600.ca
Rep. character $\chi_{1600}(111,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $944$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1600.ca (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1600, [\chi])\).

Total New Old
Modular forms 3904 976 2928
Cusp forms 3776 944 2832
Eisenstein series 128 32 96

Trace form

\( 944 q + 6 q^{3} - 8 q^{5} + 32 q^{7} + O(q^{10}) \) \( 944 q + 6 q^{3} - 8 q^{5} + 32 q^{7} + 6 q^{11} - 6 q^{13} - 12 q^{17} + 6 q^{19} - 60 q^{21} + 12 q^{23} + 42 q^{27} - 6 q^{29} - 12 q^{33} + 160 q^{35} - 6 q^{37} + 12 q^{39} - 112 q^{43} - 76 q^{45} + 5904 q^{49} - 20 q^{51} - 6 q^{53} + 272 q^{55} + 6 q^{59} - 6 q^{61} + 48 q^{65} + 438 q^{67} + 30 q^{69} + 12 q^{71} - 278 q^{75} - 300 q^{77} + 1824 q^{81} + 166 q^{83} + 42 q^{85} + 908 q^{87} + 300 q^{91} - 52 q^{93} - 12 q^{97} + 304 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1600, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)