Properties

Label 20.4.c
Level 20
Weight 4
Character orbit c
Rep. character \(\chi_{20}(9,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 20.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(20, [\chi])\).

Total New Old
Modular forms 12 2 10
Cusp forms 6 2 4
Eisenstein series 6 0 6

Trace form

\(2q \) \(\mathstrut +\mathstrut 14q^{5} \) \(\mathstrut -\mathstrut 98q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut 14q^{5} \) \(\mathstrut -\mathstrut 98q^{9} \) \(\mathstrut +\mathstrut 40q^{11} \) \(\mathstrut +\mathstrut 152q^{15} \) \(\mathstrut -\mathstrut 168q^{19} \) \(\mathstrut +\mathstrut 152q^{21} \) \(\mathstrut -\mathstrut 54q^{25} \) \(\mathstrut +\mathstrut 12q^{29} \) \(\mathstrut -\mathstrut 448q^{31} \) \(\mathstrut -\mathstrut 152q^{35} \) \(\mathstrut +\mathstrut 912q^{39} \) \(\mathstrut +\mathstrut 532q^{41} \) \(\mathstrut -\mathstrut 686q^{45} \) \(\mathstrut +\mathstrut 534q^{49} \) \(\mathstrut -\mathstrut 1216q^{51} \) \(\mathstrut +\mathstrut 280q^{55} \) \(\mathstrut -\mathstrut 56q^{59} \) \(\mathstrut +\mathstrut 364q^{61} \) \(\mathstrut -\mathstrut 912q^{65} \) \(\mathstrut -\mathstrut 1064q^{69} \) \(\mathstrut +\mathstrut 816q^{71} \) \(\mathstrut +\mathstrut 2128q^{75} \) \(\mathstrut +\mathstrut 96q^{79} \) \(\mathstrut +\mathstrut 698q^{81} \) \(\mathstrut +\mathstrut 1216q^{85} \) \(\mathstrut -\mathstrut 3052q^{89} \) \(\mathstrut -\mathstrut 912q^{91} \) \(\mathstrut -\mathstrut 1176q^{95} \) \(\mathstrut -\mathstrut 1960q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(20, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.4.c.a \(2\) \(1.180\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(14\) \(0\) \(q-\beta q^{3}+(7+\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)