Properties

Label 4032.2.c
Level 4032
Weight 2
Character orbit c
Rep. character \(\chi_{4032}(2017,\cdot)\)
Character field \(\Q\)
Dimension 60
Newforms 18
Sturm bound 1536
Trace bound 25

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 18 \)
Sturm bound: \(1536\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(23\), \(31\)

Dimensions

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

Total New Old
Modular forms 816 60 756
Cusp forms 720 60 660
Eisenstein series 96 0 96

Trace form

\( 60q + O(q^{10}) \) \( 60q + 24q^{17} - 84q^{25} - 72q^{41} + 60q^{49} + 24q^{73} + 24q^{89} + 24q^{97} + O(q^{100}) \)

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.c.a \(2\) \(32.196\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{5}-q^{7}+2iq^{11}-iq^{13}-2q^{17}+\cdots\)
4032.2.c.b \(2\) \(32.196\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+2iq^{5}-q^{7}+iq^{11}-2iq^{13}-2q^{17}+\cdots\)
4032.2.c.c \(2\) \(32.196\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{5}-q^{7}-iq^{11}-iq^{13}-2q^{17}+\cdots\)
4032.2.c.d \(2\) \(32.196\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{5}-q^{7}+2iq^{11}+iq^{13}+2q^{17}+\cdots\)
4032.2.c.e \(2\) \(32.196\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{5}-q^{7}-iq^{11}+3iq^{13}+6q^{17}+\cdots\)
4032.2.c.f \(2\) \(32.196\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+2iq^{5}+q^{7}-iq^{11}-2iq^{13}-2q^{17}+\cdots\)
4032.2.c.g \(2\) \(32.196\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{5}+q^{7}+iq^{11}-iq^{13}-2q^{17}+\cdots\)
4032.2.c.h \(2\) \(32.196\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{5}+q^{7}-2iq^{11}-iq^{13}-2q^{17}+\cdots\)
4032.2.c.i \(2\) \(32.196\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{5}+q^{7}-2iq^{11}+iq^{13}+2q^{17}+\cdots\)
4032.2.c.j \(2\) \(32.196\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{5}+q^{7}+iq^{11}+3iq^{13}+6q^{17}+\cdots\)
4032.2.c.k \(4\) \(32.196\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{12}q^{5}-q^{7}-2\zeta_{12}q^{11}+(-2\zeta_{12}+\cdots)q^{13}+\cdots\)
4032.2.c.l \(4\) \(32.196\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{12}^{3}q^{5}-q^{7}+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{11}+\cdots\)
4032.2.c.m \(4\) \(32.196\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{12}^{3}q^{5}-q^{7}+(\zeta_{12}^{2}+3\zeta_{12}^{3})q^{11}+\cdots\)
4032.2.c.n \(4\) \(32.196\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{12}q^{5}+q^{7}+2\zeta_{12}q^{11}+(-2\zeta_{12}+\cdots)q^{13}+\cdots\)
4032.2.c.o \(4\) \(32.196\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{12}^{3}q^{5}+q^{7}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{11}+\cdots\)
4032.2.c.p \(4\) \(32.196\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{12}^{3}q^{5}+q^{7}+(-\zeta_{12}^{2}-3\zeta_{12}^{3})q^{11}+\cdots\)
4032.2.c.q \(8\) \(32.196\) 8.0.897122304.10 None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{5}q^{5}-q^{7}+\beta _{5}q^{11}+(-\beta _{4}-\beta _{6}+\cdots)q^{13}+\cdots\)
4032.2.c.r \(8\) \(32.196\) 8.0.897122304.10 None \(0\) \(0\) \(0\) \(8\) \(q-\beta _{5}q^{5}+q^{7}-\beta _{5}q^{11}+(-\beta _{4}-\beta _{6}+\cdots)q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)