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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.2.k.a 35.k 35.k $4$ $0.279$ \(\Q(\zeta_{12})\) None \(-4\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12})q^{2}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
35.2.k.b 35.k 35.k $4$ $0.279$ \(\Q(\zeta_{12})\) None \(2\) \(-4\) \(4\) \(-10\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots\)