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Properties

Label 10.4.b
Level $10$
Weight $4$
Character orbit 10.b
Rep. character $\chi_{10}(9,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 10.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(10, [\chi])\).

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

Trace form

\( 2 q - 8 q^{4} - 10 q^{5} + 8 q^{6} + 46 q^{9} + 40 q^{10} - 56 q^{11} - 104 q^{14} - 40 q^{15} + 32 q^{16} + 120 q^{19} + 40 q^{20} + 104 q^{21} - 32 q^{24} - 150 q^{25} + 48 q^{26} - 180 q^{29} - 40 q^{30}+ \cdots - 1288 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
10.4.b.a 10.b 5.b $2$ $0.590$ \(\Q(\sqrt{-1}) \) None 10.4.b.a \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-\beta q^{3}-4 q^{4}+(-5\beta-5)q^{5}+\cdots\)