↑

Properties

Label 1856.4.t
Level $1856$
Weight $4$
Character orbit 1856.t
Rep. character $\chi_{1856}(655,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $356$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1856.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 464 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1856, [\chi])\).

Total New Old
Modular forms 1456 364 1092
Cusp forms 1424 356 1068
Eisenstein series 32 8 24

Trace form

\( 356 q + 4 q^{3} + 8 q^{7} + 3132 q^{9} + O(q^{10}) \) \( 356 q + 4 q^{3} + 8 q^{7} + 3132 q^{9} + 108 q^{15} - 4 q^{17} + 4 q^{19} - 112 q^{21} + 8 q^{23} + 376 q^{27} - 202 q^{29} + 604 q^{39} - 504 q^{45} + 16260 q^{49} + 108 q^{51} - 756 q^{53} + 4 q^{55} - 216 q^{57} + 4 q^{59} + 216 q^{63} - 8 q^{65} + 2040 q^{67} - 112 q^{69} + 296 q^{73} - 600 q^{79} + 26236 q^{81} + 4 q^{83} + 4 q^{87} + 88 q^{89} - 1800 q^{91} - 4380 q^{93} + 500 q^{95} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1856, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1856, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1856, [\chi]) \cong \)