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Properties

Label 35.10.b
Level $35$
Weight $10$
Character orbit 35.b
Rep. character $\chi_{35}(29,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
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: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(35, [\chi])\).

Total New Old
Modular forms 38 26 12
Cusp forms 34 26 8
Eisenstein series 4 0 4

Trace form

\( 26 q - 5460 q^{4} - 1714 q^{5} + 6156 q^{6} - 185446 q^{9} + 70264 q^{10} - 132540 q^{11} + 153664 q^{14} + 603128 q^{15} - 888268 q^{16} + 1380456 q^{19} + 5139308 q^{20} - 758716 q^{21} - 3568824 q^{24}+ \cdots - 743625048 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.10.b.a 35.b 5.b $26$ $18.026$ None 35.10.b.a \(0\) \(0\) \(-1714\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{10}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(35, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)