Properties

Label 2016.2.do
Level $2016$
Weight $2$
Character orbit 2016.do
Rep. character $\chi_{2016}(323,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $384$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2016.do (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2016, [\chi])\).

Total New Old
Modular forms 1568 384 1184
Cusp forms 1504 384 1120
Eisenstein series 64 0 64

Trace form

\( 384 q + O(q^{10}) \) \( 384 q - 32 q^{10} - 16 q^{16} - 64 q^{22} + 128 q^{46} + 128 q^{52} + 128 q^{55} - 128 q^{61} + 32 q^{67} + 96 q^{70} + 32 q^{76} + 128 q^{79} - 160 q^{88} - 192 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)