Properties

Label 4032.2.b
Level 4032
Weight 2
Character orbit b
Rep. character \(\chi_{4032}(3583,\cdot)\)
Character field \(\Q\)
Dimension 78
Newforms 18
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q\)
Newforms: \( 18 \)
Sturm bound: \(1536\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(11\), \(19\)

Dimensions

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

Total New Old
Modular forms 816 82 734
Cusp forms 720 78 642
Eisenstein series 96 4 92

Trace form

\( 78q + O(q^{10}) \) \( 78q - 74q^{25} - 12q^{29} - 20q^{37} - 2q^{49} + 4q^{53} - 16q^{65} + 36q^{77} - 64q^{85} + O(q^{100}) \)

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.b.a \(2\) \(32.196\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) \(q+(-2+\zeta_{6})q^{7}+4\zeta_{6}q^{13}-8q^{19}+\cdots\)
4032.2.b.b \(2\) \(32.196\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-2\zeta_{6}q^{5}+(-2+\zeta_{6})q^{7}+2\zeta_{6}q^{11}+\cdots\)
4032.2.b.c \(2\) \(32.196\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+(-2-\zeta_{6})q^{7}-2\zeta_{6}q^{11}+4\zeta_{6}q^{17}+\cdots\)
4032.2.b.d \(2\) \(32.196\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\beta q^{5}+(-1+\beta )q^{7}-\beta q^{11}-2\beta q^{13}+\cdots\)
4032.2.b.e \(2\) \(32.196\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{7}+2\beta q^{11}+2\beta q^{23}+5q^{25}+\cdots\)
4032.2.b.f \(2\) \(32.196\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{5}+(1-\beta )q^{7}+\beta q^{11}-2\beta q^{13}+\cdots\)
4032.2.b.g \(2\) \(32.196\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) \(q+(2+\zeta_{6})q^{7}+2\zeta_{6}q^{11}+4\zeta_{6}q^{17}+\cdots\)
4032.2.b.h \(2\) \(32.196\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) \(q-2\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}-2\zeta_{6}q^{11}+\cdots\)
4032.2.b.i \(2\) \(32.196\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) \(q+(2+\zeta_{6})q^{7}-4\zeta_{6}q^{13}+8q^{19}+5q^{25}+\cdots\)
4032.2.b.j \(4\) \(32.196\) 4.0.2312.1 None \(0\) \(0\) \(0\) \(-2\) \(q+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}-\beta _{3}q^{7}+\cdots\)
4032.2.b.k \(4\) \(32.196\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-21}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}-\beta _{3}q^{7}-\beta _{1}q^{11}-\beta _{2}q^{17}+\cdots\)
4032.2.b.l \(4\) \(32.196\) \(\Q(\sqrt{-6}, \sqrt{7})\) \(\Q(\sqrt{-21}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}-\beta _{3}q^{7}-\beta _{2}q^{11}-3\beta _{1}q^{17}+\cdots\)
4032.2.b.m \(4\) \(32.196\) \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{7}-\beta _{1}q^{11}+2\beta _{1}q^{23}+5q^{25}+\cdots\)
4032.2.b.n \(4\) \(32.196\) 4.0.2312.1 None \(0\) \(0\) \(0\) \(2\) \(q+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\beta _{3}q^{7}+\cdots\)
4032.2.b.o \(8\) \(32.196\) 8.0.836829184.2 None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{1}q^{5}-\beta _{2}q^{7}+(\beta _{2}+\beta _{4}+\beta _{7})q^{11}+\cdots\)
4032.2.b.p \(8\) \(32.196\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{5}+\zeta_{16}^{4}q^{7}+\zeta_{16}q^{11}+\cdots\)
4032.2.b.q \(8\) \(32.196\) 8.0.836829184.2 None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{5}+\beta _{2}q^{7}+(-\beta _{2}-\beta _{4}-\beta _{7})q^{11}+\cdots\)
4032.2.b.r \(16\) \(32.196\) 16.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+\beta _{8}q^{7}+(-\beta _{7}-\beta _{11})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)