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Properties

Label 35.3.g
Level $35$
Weight $3$
Character orbit 35.g
Rep. character $\chi_{35}(8,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 35.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(35, [\chi])\).

Total New Old
Modular forms 20 12 8
Cusp forms 12 12 0
Eisenstein series 8 0 8

Trace form

\( 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8} + O(q^{10}) \) \( 12 q - 4 q^{2} - 4 q^{3} - 8 q^{5} - 24 q^{6} + 24 q^{8} + 28 q^{10} - 12 q^{11} + 16 q^{12} - 4 q^{13} - 64 q^{15} + 40 q^{16} - 12 q^{17} - 56 q^{18} + 60 q^{20} + 28 q^{21} - 68 q^{22} - 16 q^{23} + 64 q^{25} - 56 q^{26} + 164 q^{27} - 76 q^{30} - 96 q^{31} + 32 q^{32} + 124 q^{33} + 232 q^{36} - 104 q^{37} + 80 q^{38} - 124 q^{40} - 208 q^{41} - 140 q^{42} + 76 q^{43} + 92 q^{45} - 80 q^{46} - 164 q^{47} - 392 q^{48} - 52 q^{50} + 220 q^{51} + 216 q^{52} - 204 q^{53} + 116 q^{55} + 168 q^{56} - 236 q^{57} + 356 q^{58} + 152 q^{60} + 280 q^{61} + 568 q^{62} + 112 q^{63} - 192 q^{65} - 544 q^{66} + 324 q^{67} + 184 q^{68} - 112 q^{70} + 144 q^{71} - 440 q^{72} - 248 q^{73} + 108 q^{75} - 632 q^{76} - 56 q^{77} + 12 q^{78} + 60 q^{80} - 260 q^{81} - 376 q^{82} - 224 q^{83} - 324 q^{85} + 456 q^{86} + 244 q^{87} - 24 q^{88} + 780 q^{90} + 84 q^{91} - 424 q^{92} + 236 q^{93} + 52 q^{95} + 504 q^{96} + 564 q^{97} + 28 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
35.3.g.a 35.g 5.c $12$ $0.954$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(-4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4}+\beta _{10}+\cdots)q^{4}+\cdots\)