Properties

Label 4032.2.h
Level 4032
Weight 2
Character orbit h
Rep. character \(\chi_{4032}(575,\cdot)\)
Character field \(\Q\)
Dimension 48
Newforms 8
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
Newforms: \( 8 \)
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 48 768
Cusp forms 720 48 672
Eisenstein series 96 0 96

Trace form

\(48q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(48q \) \(\mathstrut -\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 48q^{49} \) \(\mathstrut -\mathstrut 64q^{61} \) \(\mathstrut +\mathstrut 64q^{85} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.h.a \(4\) \(32.196\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}-\zeta_{8}^{3}q^{11}-6q^{13}+\cdots\)
4032.2.h.b \(4\) \(32.196\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+2\zeta_{8}^{3}q^{11}+5\zeta_{8}^{2}q^{17}+\cdots\)
4032.2.h.c \(4\) \(32.196\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{11}+2q^{13}+\cdots\)
4032.2.h.d \(4\) \(32.196\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{7}+3\zeta_{8}^{3}q^{11}+2q^{13}+2\zeta_{8}^{2}q^{17}+\cdots\)
4032.2.h.e \(4\) \(32.196\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+4\zeta_{8}^{3}q^{11}+4q^{13}+\cdots\)
4032.2.h.f \(8\) \(32.196\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{2}+\zeta_{24}^{7})q^{5}+\zeta_{24}q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)
4032.2.h.g \(8\) \(32.196\) 8.0.5473632256.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{5}+\beta _{6})q^{5}-\beta _{1}q^{7}+(-\beta _{4}-2\beta _{7})q^{11}+\cdots\)
4032.2.h.h \(12\) \(32.196\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+\beta _{3}q^{7}+(-\beta _{5}-\beta _{6})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)