Properties

Label 4032.2.v
Level 4032
Weight 2
Character orbit v
Rep. character \(\chi_{4032}(1583,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 96
Newforms 5
Sturm bound 1536
Trace bound 13

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Defining parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 48 \)
Character field: \(\Q(i)\)
Newforms: \( 5 \)
Sturm bound: \(1536\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

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

Total New Old
Modular forms 1600 96 1504
Cusp forms 1472 96 1376
Eisenstein series 128 0 128

Trace form

\(96q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(96q \) \(\mathstrut +\mathstrut 32q^{19} \) \(\mathstrut -\mathstrut 64q^{43} \) \(\mathstrut +\mathstrut 96q^{49} \) \(\mathstrut -\mathstrut 128q^{55} \) \(\mathstrut +\mathstrut 64q^{61} \) \(\mathstrut -\mathstrut 16q^{67} \) \(\mathstrut +\mathstrut 64q^{85} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.v.a \(4\) \(32.196\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-4\) \(q+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}-q^{7}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{11}+\cdots\)
4032.2.v.b \(4\) \(32.196\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-4\) \(q+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}-q^{7}+(2\zeta_{8}^{2}-2\zeta_{8}^{3})q^{11}+\cdots\)
4032.2.v.c \(12\) \(32.196\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(12\) \(q+(\beta _{3}-\beta _{5})q^{5}+q^{7}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{11}+\cdots\)
4032.2.v.d \(36\) \(32.196\) None \(0\) \(0\) \(0\) \(36\)
4032.2.v.e \(40\) \(32.196\) None \(0\) \(0\) \(0\) \(-40\)

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

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)