Properties

Label 4032.2.k
Level 4032
Weight 2
Character orbit k
Rep. character \(\chi_{4032}(3905,\cdot)\)
Character field \(\Q\)
Dimension 64
Newforms 8
Sturm bound 1536
Trace bound 67

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Defining parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q\)
Newforms: \( 8 \)
Sturm bound: \(1536\)
Trace bound: \(67\)
Distinguishing \(T_p\): \(5\), \(43\), \(67\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4032, [\chi])\).

Total New Old
Modular forms 816 64 752
Cusp forms 720 64 656
Eisenstein series 96 0 96

Trace form

\(64q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 64q^{25} \) \(\mathstrut -\mathstrut 32q^{37} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4032, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4032.2.k.a \(4\) \(32.196\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{3}q^{5}+(-1+\beta _{1})q^{7}-\beta _{2}q^{11}+\cdots\)
4032.2.k.b \(4\) \(32.196\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+(\beta _{1}+\beta _{3})q^{23}+\cdots\)
4032.2.k.c \(4\) \(32.196\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{11}+(-\beta _{1}-\beta _{3})q^{23}+\cdots\)
4032.2.k.d \(4\) \(32.196\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{3}q^{5}+(1-\beta _{1})q^{7}+\beta _{2}q^{11}-2\beta _{1}q^{13}+\cdots\)
4032.2.k.e \(8\) \(32.196\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\zeta_{16}^{7}q^{5}+(-1-\zeta_{16}^{6})q^{7}+(\zeta_{16}+\cdots)q^{11}+\cdots\)
4032.2.k.f \(8\) \(32.196\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(8\) \(q-\zeta_{16}^{7}q^{5}+(1+\zeta_{16}^{4})q^{7}+(\zeta_{16}+\zeta_{16}^{2}+\cdots)q^{11}+\cdots\)
4032.2.k.g \(16\) \(32.196\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+\beta _{6}q^{7}-\beta _{3}q^{11}+\beta _{13}q^{13}+\cdots\)
4032.2.k.h \(16\) \(32.196\) 16.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+\beta _{3}q^{7}+\beta _{4}q^{11}+\beta _{9}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4032, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)