Properties

Label 35.2.b
Level $35$
Weight $2$
Character orbit 35.b
Rep. character $\chi_{35}(29,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
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: \(8\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\( 2q - 4q^{4} - 4q^{5} + 4q^{6} + 4q^{9} + O(q^{10}) \) \( 2q - 4q^{4} - 4q^{5} + 4q^{6} + 4q^{9} + 4q^{10} - 6q^{11} + 4q^{14} - 2q^{15} - 8q^{16} + 8q^{20} - 2q^{21} + 6q^{25} + 4q^{26} + 10q^{29} - 8q^{30} + 4q^{31} - 28q^{34} - 2q^{35} - 8q^{36} - 2q^{39} + 4q^{41} + 12q^{44} - 8q^{45} + 24q^{46} - 2q^{49} - 16q^{50} + 14q^{51} + 20q^{54} + 12q^{55} - 20q^{59} + 4q^{60} - 16q^{61} + 16q^{64} - 2q^{65} - 12q^{66} - 12q^{69} - 8q^{70} - 16q^{71} - 8q^{74} + 8q^{75} + 10q^{79} + 16q^{80} + 2q^{81} + 4q^{84} + 14q^{85} - 16q^{86} + 8q^{90} - 2q^{91} + 12q^{94} - 16q^{96} - 12q^{99} + O(q^{100}) \)

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.b.a \(2\) \(0.279\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+2iq^{2}-iq^{3}-2q^{4}+(-2-i)q^{5}+\cdots\)