Properties

Label 42.3.c
Level $42$
Weight $3$
Character orbit 42.c
Rep. character $\chi_{42}(13,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 42.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(42, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 12 4 8
Eisenstein series 8 0 8

Trace form

\( 4q + 8q^{4} + 8q^{7} - 12q^{9} + O(q^{10}) \) \( 4q + 8q^{4} + 8q^{7} - 12q^{9} - 24q^{11} - 24q^{14} - 24q^{15} + 16q^{16} + 12q^{21} - 24q^{22} + 24q^{23} + 28q^{25} + 16q^{28} + 120q^{29} + 24q^{30} - 24q^{35} - 24q^{36} - 80q^{37} + 96q^{39} + 48q^{42} - 128q^{43} - 48q^{44} - 72q^{46} - 20q^{49} + 96q^{50} - 24q^{51} - 216q^{53} - 48q^{56} - 24q^{57} - 48q^{60} - 24q^{63} + 32q^{64} + 240q^{65} + 176q^{67} + 72q^{70} - 120q^{71} + 288q^{74} + 24q^{77} - 48q^{78} + 128q^{79} + 36q^{81} + 24q^{84} + 216q^{85} - 240q^{86} - 48q^{88} + 48q^{92} - 144q^{93} - 240q^{95} - 192q^{98} + 72q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(42, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
42.3.c.a \(4\) \(1.144\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+(-2\beta _{2}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(42, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(42, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)