Properties

Label 35.2.f
Level $35$
Weight $2$
Character orbit 35.f
Rep. character $\chi_{35}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 35.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
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

\( 4q - 4q^{2} + 4q^{7} - 8q^{8} + O(q^{10}) \) \( 4q - 4q^{2} + 4q^{7} - 8q^{8} - 4q^{11} + 16q^{16} + 8q^{18} - 20q^{21} + 4q^{22} + 8q^{23} - 20q^{30} + 20q^{35} - 24q^{37} + 20q^{42} - 12q^{43} - 16q^{46} + 20q^{50} + 20q^{51} + 4q^{53} - 16q^{56} + 20q^{57} + 12q^{58} - 8q^{63} - 4q^{67} - 20q^{70} - 24q^{71} - 16q^{72} - 4q^{77} - 20q^{78} + 44q^{81} - 20q^{85} + 24q^{86} + 8q^{88} + 20q^{91} + 20q^{93} - 20q^{95} - 12q^{98} + O(q^{100}) \)

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.f.a \(4\) \(0.279\) \(\Q(i, \sqrt{10})\) None \(-4\) \(0\) \(0\) \(4\) \(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)