Properties

Label 42.2.f
Level $42$
Weight $2$
Character orbit 42.f
Rep. character $\chi_{42}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 42.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

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

\( 4q + 2q^{4} - 10q^{7} - 6q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 10q^{7} - 6q^{9} - 6q^{10} + 12q^{15} - 2q^{16} + 12q^{19} + 12q^{22} + 6q^{24} + 4q^{25} - 2q^{28} - 6q^{31} - 18q^{33} - 12q^{36} + 4q^{37} - 6q^{40} - 6q^{42} - 32q^{43} - 12q^{46} + 22q^{49} + 12q^{51} + 12q^{52} + 18q^{54} + 6q^{58} + 6q^{60} + 24q^{63} - 4q^{64} - 4q^{67} + 18q^{70} + 24q^{73} - 24q^{78} + 2q^{79} - 18q^{81} - 24q^{82} - 24q^{85} - 18q^{87} + 6q^{88} - 12q^{91} - 24q^{94} + 6q^{96} + O(q^{100}) \)

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.f.a \(4\) \(0.335\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-10\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)

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

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