Properties

Label 35.3.i
Level $35$
Weight $3$
Character orbit 35.i
Rep. character $\chi_{35}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 35.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(35, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

Trace form

\( 12 q + 6 q^{4} - 18 q^{9} + O(q^{10}) \) \( 12 q + 6 q^{4} - 18 q^{9} - 54 q^{10} + 6 q^{11} - 66 q^{14} + 48 q^{15} - 6 q^{16} + 18 q^{19} + 12 q^{21} + 216 q^{24} + 18 q^{25} + 18 q^{26} + 48 q^{30} - 108 q^{31} + 222 q^{35} - 204 q^{36} - 240 q^{39} - 162 q^{40} - 42 q^{44} - 216 q^{45} + 114 q^{46} - 324 q^{49} - 192 q^{50} + 180 q^{51} + 252 q^{54} + 336 q^{56} + 396 q^{59} + 384 q^{60} - 108 q^{61} + 372 q^{64} - 54 q^{65} - 108 q^{66} + 300 q^{70} + 192 q^{71} - 594 q^{74} - 216 q^{75} - 192 q^{79} - 504 q^{80} + 294 q^{81} - 1200 q^{84} - 192 q^{85} - 384 q^{86} + 684 q^{89} - 72 q^{91} + 990 q^{94} + 288 q^{95} - 540 q^{96} + 396 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.3.i.a $12$ $0.954$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{11})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)