↑

Properties

Label 1088.2.cd
Level $1088$
Weight $2$
Character orbit 1088.cd
Rep. character $\chi_{1088}(79,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $272$
Sturm bound $288$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1088 = 2^{6} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1088.cd (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 272 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1088, [\chi])\).

Total New Old
Modular forms 1216 304 912
Cusp forms 1088 272 816
Eisenstein series 128 32 96

Trace form

\( 272 q + 8 q^{3} - 8 q^{5} + 16 q^{7} + O(q^{10}) \) \( 272 q + 8 q^{3} - 8 q^{5} + 16 q^{7} + 8 q^{11} - 16 q^{17} - 24 q^{19} + 16 q^{23} + 8 q^{27} - 8 q^{29} + 16 q^{35} - 8 q^{37} + 16 q^{39} + 8 q^{43} - 8 q^{45} - 16 q^{49} + 88 q^{51} - 8 q^{53} + 16 q^{55} + 8 q^{59} - 72 q^{61} - 48 q^{63} - 48 q^{65} - 16 q^{69} + 16 q^{71} + 8 q^{75} - 8 q^{77} - 16 q^{81} + 88 q^{83} - 8 q^{85} + 16 q^{87} - 48 q^{91} - 8 q^{93} - 16 q^{97} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1088, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1088, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1088, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(544, [\chi])\)\(^{\oplus 2}\)