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Properties

Label 29.2.d
Level $29$
Weight $2$
Character orbit 29.d
Rep. character $\chi_{29}(7,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $6$
Newform subspaces $1$
Sturm bound $5$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 29.d (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(29, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 6 6 0
Eisenstein series 12 12 0

Trace form

\( 6 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} + q^{7} - 7 q^{8} + 6 q^{9} + O(q^{10}) \) \( 6 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + q^{5} - 3 q^{6} + q^{7} - 7 q^{8} + 6 q^{9} + 9 q^{10} - 11 q^{11} + 4 q^{12} - 5 q^{13} + 9 q^{14} + 5 q^{15} + 4 q^{16} + 8 q^{17} - 9 q^{18} + q^{19} + 2 q^{20} + 5 q^{21} + 6 q^{22} - 7 q^{23} + 7 q^{24} - 24 q^{25} + 4 q^{26} - 11 q^{27} - 12 q^{28} + 6 q^{29} - 18 q^{30} + 5 q^{31} - 13 q^{32} + q^{33} + 2 q^{34} - q^{35} + 5 q^{36} + 11 q^{37} + 2 q^{38} + 3 q^{39} + 14 q^{40} + 20 q^{41} - 4 q^{42} + 13 q^{43} + 20 q^{44} + q^{45} + 11 q^{47} + 6 q^{48} - 22 q^{49} + q^{50} - 2 q^{51} - 10 q^{52} + 3 q^{53} + 6 q^{54} - 17 q^{55} - 7 q^{56} - 2 q^{57} - 16 q^{58} - 56 q^{59} - 4 q^{60} + 3 q^{61} + 3 q^{62} + 15 q^{63} + q^{64} + 5 q^{65} - 5 q^{66} + 19 q^{67} - 12 q^{68} - 7 q^{69} - 2 q^{70} + 21 q^{71} - 25 q^{73} - 6 q^{74} + 48 q^{75} - 5 q^{76} + 11 q^{77} + 13 q^{78} - 9 q^{79} - 18 q^{80} + 18 q^{81} - 2 q^{82} + 17 q^{83} + 3 q^{84} - 8 q^{85} - 16 q^{86} - 5 q^{87} + 42 q^{88} + 7 q^{89} + 2 q^{90} + 5 q^{91} - 17 q^{93} + 8 q^{94} + 13 q^{95} - 2 q^{96} + q^{97} + 19 q^{98} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(29, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
29.2.d.a 29.d 29.d $6$ $0.232$ \(\Q(\zeta_{14})\) None \(-2\) \(-5\) \(1\) \(1\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)