Properties

Label 42.2.e
Level 42
Weight 2
Character orbit e
Rep. character \(\chi_{42}(25,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 4
Newforms 2
Sturm bound 16
Trace bound 2

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Defining parameters

Level: \( N \) = \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 42.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(42, [\chi])\).

Total New Old
Modular forms 24 4 20
Cusp forms 8 4 4
Eisenstein series 16 0 16

Trace form

\(4q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 4q^{36} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut -\mathstrut 8q^{44} \) \(\mathstrut -\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 4q^{52} \) \(\mathstrut +\mathstrut 12q^{53} \) \(\mathstrut +\mathstrut 2q^{54} \) \(\mathstrut +\mathstrut 28q^{55} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 24q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 8q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut +\mathstrut 16q^{61} \) \(\mathstrut +\mathstrut 8q^{62} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 4q^{68} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut +\mathstrut 8q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut -\mathstrut 8q^{84} \) \(\mathstrut -\mathstrut 8q^{85} \) \(\mathstrut -\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut -\mathstrut 2q^{88} \) \(\mathstrut -\mathstrut 4q^{90} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut +\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(42, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
42.2.e.a \(2\) \(0.335\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(1\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-1+\cdots)q^{5}+\cdots\)
42.2.e.b \(2\) \(0.335\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-3\) \(5\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+(-3+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(42, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(42, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)