Properties

Label 4020.2.q
Level $4020$
Weight $2$
Character orbit 4020.q
Rep. character $\chi_{4020}(841,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $92$
Newform subspaces $13$
Sturm bound $1632$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4020.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 13 \)
Sturm bound: \(1632\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4020, [\chi])\).

Total New Old
Modular forms 1656 92 1564
Cusp forms 1608 92 1516
Eisenstein series 48 0 48

Trace form

\( 92 q + 4 q^{3} - 4 q^{7} + 92 q^{9} + O(q^{10}) \) \( 92 q + 4 q^{3} - 4 q^{7} + 92 q^{9} - 4 q^{11} - 10 q^{13} + 8 q^{17} - 4 q^{21} + 12 q^{23} + 92 q^{25} + 4 q^{27} + 20 q^{29} - 2 q^{31} - 4 q^{35} - 4 q^{37} + 2 q^{39} + 4 q^{41} - 20 q^{43} - 20 q^{47} - 50 q^{49} + 4 q^{51} - 16 q^{53} + 12 q^{55} - 16 q^{57} - 56 q^{59} + 10 q^{61} - 4 q^{63} + 8 q^{65} - 46 q^{67} - 8 q^{69} - 8 q^{71} + 10 q^{73} + 4 q^{75} + 8 q^{77} - 10 q^{79} + 92 q^{81} - 4 q^{83} - 12 q^{85} + 4 q^{87} + 64 q^{89} - 8 q^{91} - 14 q^{93} - 30 q^{97} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4020, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4020.2.q.a 4020.q 67.c $2$ $32.100$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{3}+q^{5}-3\zeta_{6}q^{7}+q^{9}-5\zeta_{6}q^{11}+\cdots\)
4020.2.q.b 4020.q 67.c $2$ $32.100$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{3}+q^{5}-3\zeta_{6}q^{7}+q^{9}+5\zeta_{6}q^{11}+\cdots\)
4020.2.q.c 4020.q 67.c $2$ $32.100$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{3}+q^{5}+\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
4020.2.q.d 4020.q 67.c $2$ $32.100$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{3}+q^{5}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+\cdots\)
4020.2.q.e 4020.q 67.c $2$ $32.100$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{3}-q^{5}-\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
4020.2.q.f 4020.q 67.c $2$ $32.100$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{3}-q^{5}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+\cdots\)
4020.2.q.g 4020.q 67.c $2$ $32.100$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{3}-q^{5}-\zeta_{6}q^{7}+q^{9}+5\zeta_{6}q^{11}+\cdots\)
4020.2.q.h 4020.q 67.c $2$ $32.100$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{3}-q^{5}+\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
4020.2.q.i 4020.q 67.c $4$ $32.100$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(4\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{3}-q^{5}+(-\beta _{1}+\beta _{3})q^{7}+q^{9}+\cdots\)
4020.2.q.j 4020.q 67.c $12$ $32.100$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(12\) \(-12\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{3}-q^{5}+(\beta _{1}-\beta _{6}-\beta _{9})q^{7}+q^{9}+\cdots\)
4020.2.q.k 4020.q 67.c $14$ $32.100$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-14\) \(14\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{3}+q^{5}-\beta _{6}q^{7}+q^{9}+(1-\beta _{5}+\cdots)q^{11}+\cdots\)
4020.2.q.l 4020.q 67.c $22$ $32.100$ None \(0\) \(-22\) \(-22\) \(1\) $\mathrm{SU}(2)[C_{3}]$
4020.2.q.m 4020.q 67.c $24$ $32.100$ None \(0\) \(24\) \(24\) \(-3\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(4020, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4020, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(134, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(268, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(402, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(670, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(804, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1340, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2010, [\chi])\)\(^{\oplus 2}\)