Properties

Label 35.2.k
Level $35$
Weight $2$
Character orbit 35.k
Rep. character $\chi_{35}(3,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $8$
Newform subspaces $2$
Sturm bound $8$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 35.k (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 24 24 0
Cusp forms 8 8 0
Eisenstein series 16 16 0

Trace form

\( 8q - 2q^{2} - 6q^{3} - 10q^{7} - 4q^{8} + O(q^{10}) \) \( 8q - 2q^{2} - 6q^{3} - 10q^{7} - 4q^{8} + 6q^{10} + 4q^{11} + 6q^{12} - 12q^{15} - 4q^{16} + 12q^{17} + 4q^{18} + 20q^{21} + 8q^{22} + 10q^{23} - 12q^{25} - 24q^{26} + 18q^{28} + 8q^{30} - 24q^{31} - 18q^{32} - 8q^{35} - 24q^{36} - 12q^{38} + 18q^{40} - 26q^{42} - 12q^{43} + 24q^{45} + 28q^{46} + 24q^{47} + 28q^{50} - 8q^{51} + 24q^{52} + 20q^{53} + 16q^{56} + 16q^{57} - 6q^{58} - 6q^{60} - 24q^{61} - 4q^{63} - 24q^{65} - 12q^{66} - 14q^{67} - 12q^{68} - 40q^{70} + 24q^{71} - 8q^{72} - 24q^{73} - 6q^{75} - 20q^{77} + 32q^{78} - 24q^{80} - 8q^{81} - 6q^{82} + 8q^{85} + 36q^{86} + 18q^{87} - 8q^{88} + 40q^{91} - 36q^{92} + 4q^{93} + 8q^{95} + 60q^{96} + 18q^{98} + O(q^{100}) \)

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.k.a \(4\) \(0.279\) \(\Q(\zeta_{12})\) None \(-4\) \(-2\) \(-4\) \(0\) \(q+(-1+\zeta_{12})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
35.2.k.b \(4\) \(0.279\) \(\Q(\zeta_{12})\) None \(2\) \(-4\) \(4\) \(-10\) \(q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots\)