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Properties

Label 29.4.b
Level $29$
Weight $4$
Character orbit 29.b
Rep. character $\chi_{29}(28,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
Sturm bound $10$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 29.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(29, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 6 6 0
Eisenstein series 2 2 0

Trace form

\( 6 q - 28 q^{4} + 22 q^{5} - 12 q^{6} - 28 q^{7} + 40 q^{9} + O(q^{10}) \) \( 6 q - 28 q^{4} + 22 q^{5} - 12 q^{6} - 28 q^{7} + 40 q^{9} + 30 q^{13} + 244 q^{16} - 548 q^{20} - 204 q^{22} - 76 q^{23} + 236 q^{24} + 24 q^{25} + 576 q^{28} - 54 q^{29} + 204 q^{30} + 166 q^{33} + 512 q^{34} - 796 q^{35} - 1184 q^{36} + 920 q^{38} - 192 q^{42} + 344 q^{45} - 1234 q^{49} + 1444 q^{51} - 1796 q^{52} + 990 q^{53} - 1204 q^{54} + 1028 q^{57} + 1600 q^{58} + 1260 q^{59} + 3076 q^{62} - 384 q^{63} - 3228 q^{64} - 1378 q^{65} - 664 q^{67} - 896 q^{71} - 3248 q^{74} - 3204 q^{78} + 6588 q^{80} - 1230 q^{81} + 4272 q^{82} - 2244 q^{83} - 780 q^{86} + 1772 q^{87} + 7932 q^{88} + 1348 q^{91} - 768 q^{92} - 3718 q^{93} - 3852 q^{94} + 1260 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(29, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
29.4.b.a 29.b 29.b $6$ $1.711$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(22\) \(-28\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-5+\beta _{4}+\beta _{5})q^{4}+\cdots\)