Properties

Label 42.4.f
Level $42$
Weight $4$
Character orbit 42.f
Rep. character $\chi_{42}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(42, [\chi])\).

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

Trace form

\( 16q + 32q^{4} + 80q^{7} + 18q^{9} + O(q^{10}) \) \( 16q + 32q^{4} + 80q^{7} + 18q^{9} - 36q^{10} - 128q^{16} - 48q^{18} - 342q^{19} - 450q^{21} + 24q^{22} - 48q^{24} - 194q^{25} + 88q^{28} + 360q^{30} + 804q^{31} + 1332q^{33} + 144q^{36} - 962q^{37} + 594q^{39} - 144q^{40} - 180q^{42} + 1732q^{43} - 2394q^{45} + 168q^{46} + 820q^{49} + 1638q^{51} + 744q^{52} + 180q^{54} - 2664q^{57} - 780q^{58} - 4620q^{61} - 2016q^{63} - 1024q^{64} - 2016q^{66} - 706q^{67} - 60q^{70} + 192q^{72} + 3294q^{73} + 6174q^{75} + 2832q^{78} - 2656q^{79} + 126q^{81} + 432q^{82} - 432q^{84} + 5232q^{85} + 1026q^{87} + 48q^{88} + 4098q^{91} + 2016q^{93} + 3888q^{94} - 192q^{96} - 4284q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(42, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
42.4.f.a \(16\) \(2.478\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(80\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(4+4\beta _{5})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(42, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(42, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)