Properties

Label 42.2.e
Level $42$
Weight $2$
Character orbit 42.e
Rep. character $\chi_{42}(25,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
Newform subspaces $2$
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: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(42, [\chi])\) into newform subspaces

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

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