Properties

Label 4032.2.p
Level 4032
Weight 2
Character orbit p
Rep. character \(\chi_{4032}(1567,\cdot)\)
Character field \(\Q\)
Dimension 80
Newforms 11
Sturm bound 1536
Trace bound 25

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Defining parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 56 \)
Character field: \(\Q\)
Newforms: \( 11 \)
Sturm bound: \(1536\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 816 80 736
Cusp forms 720 80 640
Eisenstein series 96 0 96

Trace form

\(80q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(80q \) \(\mathstrut +\mathstrut 80q^{25} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.p.a \(4\) \(32.196\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}+(-\beta _{1}-2\beta _{2})q^{11}-4q^{13}+\cdots\)
4032.2.p.b \(4\) \(32.196\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{7}-2q^{13}+(-2\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{19}+\cdots\)
4032.2.p.c \(4\) \(32.196\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{7}+2q^{13}+(2\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{19}+\cdots\)
4032.2.p.d \(4\) \(32.196\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}-2\beta _{2})q^{11}+\cdots\)
4032.2.p.e \(8\) \(32.196\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{4}q^{5}+\zeta_{24}^{5}q^{7}+\zeta_{24}^{3}q^{11}+\cdots\)
4032.2.p.f \(8\) \(32.196\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{6}q^{5}-\zeta_{24}^{4}q^{7}-\zeta_{24}^{3}q^{11}+\cdots\)
4032.2.p.g \(8\) \(32.196\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{6}q^{5}+\zeta_{24}^{4}q^{7}-\zeta_{24}^{3}q^{11}+\cdots\)
4032.2.p.h \(8\) \(32.196\) 8.0.629407744.1 \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}-\beta _{4}q^{7}+(-\beta _{1}+\beta _{6})q^{13}+\cdots\)
4032.2.p.i \(8\) \(32.196\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{4}q^{5}-\zeta_{24}^{5}q^{7}-\zeta_{24}^{3}q^{11}+\cdots\)
4032.2.p.j \(12\) \(32.196\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+\beta _{10}q^{7}+\beta _{11}q^{11}-2q^{13}+\cdots\)
4032.2.p.k \(12\) \(32.196\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}-\beta _{10}q^{7}+\beta _{11}q^{11}+2q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)