Properties

Label 4020.2.q
Level 4020
Weight 2
Character orbit q
Rep. character \(\chi_{4020}(841,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 92
Newforms 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: \(\Q(\zeta_{3})\)
Newforms: \( 13 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(4020, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4020.2.q.a \(2\) \(32.100\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(-3\) \(q-q^{3}+q^{5}-3\zeta_{6}q^{7}+q^{9}-5\zeta_{6}q^{11}+\cdots\)
4020.2.q.b \(2\) \(32.100\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(-3\) \(q-q^{3}+q^{5}-3\zeta_{6}q^{7}+q^{9}+5\zeta_{6}q^{11}+\cdots\)
4020.2.q.c \(2\) \(32.100\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(1\) \(q-q^{3}+q^{5}+\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
4020.2.q.d \(2\) \(32.100\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(1\) \(q-q^{3}+q^{5}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+\cdots\)
4020.2.q.e \(2\) \(32.100\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-2\) \(-1\) \(q+q^{3}-q^{5}-\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
4020.2.q.f \(2\) \(32.100\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-2\) \(-1\) \(q+q^{3}-q^{5}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}q^{11}+\cdots\)
4020.2.q.g \(2\) \(32.100\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-2\) \(-1\) \(q+q^{3}-q^{5}-\zeta_{6}q^{7}+q^{9}+5\zeta_{6}q^{11}+\cdots\)
4020.2.q.h \(2\) \(32.100\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-2\) \(1\) \(q+q^{3}-q^{5}+\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
4020.2.q.i \(4\) \(32.100\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(4\) \(-4\) \(-1\) \(q+q^{3}-q^{5}+(-\beta _{1}+\beta _{3})q^{7}+q^{9}+\cdots\)
4020.2.q.j \(12\) \(32.100\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(12\) \(-12\) \(2\) \(q+q^{3}-q^{5}+(\beta _{1}-\beta _{6}-\beta _{9})q^{7}+q^{9}+\cdots\)
4020.2.q.k \(14\) \(32.100\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-14\) \(14\) \(3\) \(q-q^{3}+q^{5}-\beta _{6}q^{7}+q^{9}+(1-\beta _{5}+\cdots)q^{11}+\cdots\)
4020.2.q.l \(22\) \(32.100\) None \(0\) \(-22\) \(-22\) \(1\)
4020.2.q.m \(24\) \(32.100\) None \(0\) \(24\) \(24\) \(-3\)

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

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