Properties

Label 4032.2.i
Level 4032
Weight 2
Character orbit i
Rep. character \(\chi_{4032}(1889,\cdot)\)
Character field \(\Q\)
Dimension 64
Newforms 3
Sturm bound 1536
Trace bound 47

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Defining parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(1536\)
Trace bound: \(47\)
Distinguishing \(T_p\): \(5\), \(47\)

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

\(64q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut -\mathstrut 64q^{25} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.i.a \(8\) \(32.196\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\beta _{3}q^{11}+\cdots\)
4032.2.i.b \(8\) \(32.196\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}+(-\beta _{2}-\beta _{4})q^{7}-\beta _{3}q^{11}+\cdots\)
4032.2.i.c \(48\) \(32.196\) None \(0\) \(0\) \(0\) \(0\)

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

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