Properties

Label 2016.2.b
Level 2016
Weight 2
Character orbit b
Rep. character \(\chi_{2016}(1567,\cdot)\)
Character field \(\Q\)
Dimension 40
Newforms 4
Sturm bound 768
Trace bound 7

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Defining parameters

Level: \( N \) = \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2016.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(768\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(19\)

Dimensions

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

Total New Old
Modular forms 416 40 376
Cusp forms 352 40 312
Eisenstein series 64 0 64

Trace form

\(40q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(40q \) \(\mathstrut -\mathstrut 56q^{25} \) \(\mathstrut +\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 16q^{53} \) \(\mathstrut -\mathstrut 48q^{77} \) \(\mathstrut +\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.b.a \(8\) \(16.098\) 8.0.836829184.2 None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{1}q^{5}+\beta _{4}q^{7}+(\beta _{2}+\beta _{4}+\beta _{7})q^{11}+\cdots\)
2016.2.b.b \(8\) \(16.098\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{5}+\zeta_{16}^{6}q^{7}-\zeta_{16}q^{11}+\cdots\)
2016.2.b.c \(8\) \(16.098\) 8.0.836829184.2 None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{5}-\beta _{4}q^{7}+(-\beta _{2}-\beta _{4}-\beta _{7})q^{11}+\cdots\)
2016.2.b.d \(16\) \(16.098\) 16.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}-\beta _{8}q^{7}+(\beta _{7}+\beta _{11})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)