Properties

Label 35.4.b
Level $35$
Weight $4$
Character orbit 35.b
Rep. character $\chi_{35}(29,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $1$
Sturm bound $16$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 35.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(35, [\chi])\).

Total New Old
Modular forms 14 10 4
Cusp forms 10 10 0
Eisenstein series 4 0 4

Trace form

\( 10 q - 36 q^{4} + 6 q^{5} + 12 q^{6} - 46 q^{9} + O(q^{10}) \) \( 10 q - 36 q^{4} + 6 q^{5} + 12 q^{6} - 46 q^{9} - 16 q^{10} + 84 q^{11} - 56 q^{14} + 8 q^{15} + 148 q^{16} + 72 q^{19} - 68 q^{20} + 140 q^{21} + 72 q^{24} - 362 q^{25} - 620 q^{26} + 88 q^{29} + 52 q^{30} + 120 q^{31} + 964 q^{34} - 28 q^{35} - 420 q^{36} + 212 q^{39} + 1396 q^{40} - 852 q^{41} - 1424 q^{44} - 510 q^{45} + 176 q^{46} - 490 q^{49} + 1644 q^{50} + 1276 q^{51} - 996 q^{54} - 1136 q^{55} + 588 q^{56} + 864 q^{59} - 1692 q^{60} - 884 q^{61} - 2724 q^{64} + 520 q^{65} + 1148 q^{66} + 4808 q^{69} + 756 q^{70} + 880 q^{71} + 3024 q^{74} + 720 q^{75} - 2672 q^{76} - 3580 q^{79} - 2316 q^{80} - 302 q^{81} - 1904 q^{84} + 1572 q^{85} + 2432 q^{86} - 1492 q^{89} - 7748 q^{90} + 476 q^{91} + 1652 q^{94} - 1628 q^{95} + 4080 q^{96} - 5304 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.4.b.a 35.b 5.b $10$ $2.065$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 35.4.b.a \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-4+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)