Properties

Label 4032.2.p
Level $4032$
Weight $2$
Character orbit 4032.p
Rep. character $\chi_{4032}(1567,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $11$
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.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
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 80 736
Cusp forms 720 80 640
Eisenstein series 96 0 96

Trace form

\( 80 q + O(q^{10}) \) \( 80 q + 80 q^{25} + 16 q^{49} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4032, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4032.2.p.a 4032.p 56.e $4$ $32.196$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{7}+(-\beta _{1}-2\beta _{2})q^{11}-4q^{13}+\cdots\)
4032.2.p.b 4032.p 56.e $4$ $32.196$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{12}^{2}q^{7}-2q^{13}+(-2\zeta_{12}+2\zeta_{12}^{2}+\cdots)q^{19}+\cdots\)
4032.2.p.c 4032.p 56.e $4$ $32.196$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{12}q^{7}+2q^{13}+(2\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{19}+\cdots\)
4032.2.p.d 4032.p 56.e $4$ $32.196$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}-2\beta _{2})q^{11}+\cdots\)
4032.2.p.e 4032.p 56.e $8$ $32.196$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{4}q^{5}+\zeta_{24}^{5}q^{7}+\zeta_{24}^{3}q^{11}+\cdots\)
4032.2.p.f 4032.p 56.e $8$ $32.196$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{6}q^{5}-\zeta_{24}^{4}q^{7}-\zeta_{24}^{3}q^{11}+\cdots\)
4032.2.p.g 4032.p 56.e $8$ $32.196$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{24}^{6}q^{5}+\zeta_{24}^{4}q^{7}-\zeta_{24}^{3}q^{11}+\cdots\)
4032.2.p.h 4032.p 56.e $8$ $32.196$ 8.0.629407744.1 \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{5}-\beta _{4}q^{7}+(-\beta _{1}+\beta _{6})q^{13}+\cdots\)
4032.2.p.i 4032.p 56.e $8$ $32.196$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{4}q^{5}-\zeta_{24}^{5}q^{7}-\zeta_{24}^{3}q^{11}+\cdots\)
4032.2.p.j 4032.p 56.e $12$ $32.196$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}+\beta _{10}q^{7}+\beta _{11}q^{11}-2q^{13}+\cdots\)
4032.2.p.k 4032.p 56.e $12$ $32.196$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}-\beta _{10}q^{7}+\beta _{11}q^{11}+2q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4032, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1344, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2016, [\chi])\)\(^{\oplus 2}\)