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 $0$

Related objects

Downloads

Learn more about

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

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

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 \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{11})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)