Properties

Label 35.2.j
Level $35$
Weight $2$
Character orbit 35.j
Rep. character $\chi_{35}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 35.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(35, [\chi])\).

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

Trace form

\( 4q - 2q^{4} - 2q^{5} - 4q^{6} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{4} - 2q^{5} - 4q^{6} - 4q^{9} - 4q^{10} + 8q^{14} + 8q^{15} + 2q^{16} + 12q^{19} + 4q^{20} - 10q^{21} + 6q^{24} + 6q^{25} - 4q^{26} - 28q^{29} + 2q^{30} - 4q^{31} - 8q^{34} - 16q^{35} + 8q^{36} - 4q^{39} - 12q^{40} + 20q^{41} - 4q^{45} + 6q^{46} + 26q^{49} + 16q^{50} + 4q^{51} + 10q^{54} + 6q^{56} + 20q^{59} - 4q^{60} - 14q^{61} - 28q^{64} + 8q^{65} - 12q^{69} - 10q^{70} - 8q^{71} - 16q^{74} - 8q^{75} - 24q^{76} - 4q^{79} + 2q^{80} - 2q^{81} + 8q^{84} + 16q^{85} - 14q^{86} + 18q^{89} + 16q^{90} - 4q^{91} + 12q^{95} + 10q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
35.2.j.a \(4\) \(0.279\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)