Properties

Label 2016.2.i
Level 2016
Weight 2
Character orbit i
Rep. character \(\chi_{2016}(881,\cdot)\)
Character field \(\Q\)
Dimension 32
Newforms 2
Sturm bound 768
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2016.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(768\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 416 32 384
Cusp forms 352 32 320
Eisenstein series 64 0 64

Trace form

\(32q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut -\mathstrut 32q^{25} \) \(\mathstrut -\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2016, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2016.2.i.a \(8\) \(16.098\) 8.0.157351936.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{7}+(-\beta _{4}-\beta _{7})q^{11}+(\beta _{5}+\beta _{6}+\cdots)q^{23}+\cdots\)
2016.2.i.b \(24\) \(16.098\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)