Properties

Label 20.3.d
Level $20$
Weight $3$
Character orbit 20.d
Rep. character $\chi_{20}(19,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $9$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 20.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(9\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(20, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4q - 4q^{5} - 16q^{6} - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{5} - 16q^{6} - 4q^{9} + 16q^{10} + 16q^{14} + 64q^{16} - 64q^{20} - 32q^{21} - 64q^{24} + 36q^{25} - 96q^{26} + 40q^{29} + 80q^{30} + 64q^{34} + 128q^{36} - 64q^{40} + 88q^{41} - 124q^{45} - 176q^{46} - 164q^{49} + 96q^{50} + 32q^{54} + 64q^{56} - 72q^{61} + 192q^{65} + 352q^{69} - 80q^{70} - 96q^{74} - 64q^{80} - 28q^{81} - 128q^{84} - 128q^{85} + 304q^{86} - 440q^{89} - 144q^{90} + 16q^{94} - 256q^{96} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
20.3.d.a \(1\) \(0.545\) \(\Q\) \(\Q(\sqrt{-5}) \) \(-2\) \(4\) \(-5\) \(-4\) \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.b \(1\) \(0.545\) \(\Q\) \(\Q(\sqrt{-5}) \) \(2\) \(-4\) \(-5\) \(4\) \(q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.c \(2\) \(0.545\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) \(q+iq^{2}-4q^{4}+(3-2i)q^{5}-4iq^{8}+\cdots\)