Properties

Label 4032.2.j
Level 4032
Weight 2
Character orbit j
Rep. character \(\chi_{4032}(2591,\cdot)\)
Character field \(\Q\)
Dimension 48
Newforms 6
Sturm bound 1536
Trace bound 43

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Defining parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(1536\)
Trace bound: \(43\)
Distinguishing \(T_p\): \(5\), \(19\), \(43\)

Dimensions

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

Total New Old
Modular forms 816 48 768
Cusp forms 720 48 672
Eisenstein series 96 0 96

Trace form

\( 48q + O(q^{10}) \) \( 48q + 48q^{25} - 48q^{49} + O(q^{100}) \)

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.j.a \(4\) \(32.196\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}-\zeta_{8}^{2}q^{11}-2\zeta_{8}q^{13}+\cdots\)
4032.2.j.b \(4\) \(32.196\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{7}-\zeta_{8}^{2}q^{11}-6\zeta_{8}q^{13}-\zeta_{8}^{3}q^{23}+\cdots\)
4032.2.j.c \(4\) \(32.196\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{7}+\zeta_{8}^{2}q^{11}+6\zeta_{8}q^{13}-\zeta_{8}^{3}q^{23}+\cdots\)
4032.2.j.d \(4\) \(32.196\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}-\zeta_{8}^{2}q^{11}+2\zeta_{8}q^{13}+\cdots\)
4032.2.j.e \(16\) \(32.196\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{13}q^{5}+\beta _{1}q^{7}+\beta _{9}q^{11}-\beta _{5}q^{13}+\cdots\)
4032.2.j.f \(16\) \(32.196\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{12}q^{5}+\beta _{8}q^{7}+(-\beta _{11}-\beta _{13}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)