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Properties

Label 29.6.a
Level $29$
Weight $6$
Character orbit 29.a
Rep. character $\chi_{29}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $2$
Sturm bound $15$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(15\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(29))\).

Total New Old
Modular forms 13 11 2
Cusp forms 11 11 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(29\)Dim.
\(+\)\(4\)
\(-\)\(7\)

Trace form

\( 11 q + 4 q^{2} - 2 q^{3} + 164 q^{4} - 36 q^{5} - 172 q^{6} - 24 q^{7} + 438 q^{8} + 725 q^{9} + O(q^{10}) \) \( 11 q + 4 q^{2} - 2 q^{3} + 164 q^{4} - 36 q^{5} - 172 q^{6} - 24 q^{7} + 438 q^{8} + 725 q^{9} + 134 q^{10} + 982 q^{11} + 234 q^{12} - 52 q^{13} - 1240 q^{14} + 318 q^{15} - 172 q^{16} - 690 q^{17} - 2390 q^{18} + 1896 q^{19} - 3528 q^{20} - 3208 q^{21} - 576 q^{22} - 5724 q^{23} + 2468 q^{24} + 7351 q^{25} - 15082 q^{26} + 8410 q^{27} - 452 q^{28} + 2523 q^{29} - 8548 q^{30} - 11418 q^{31} + 14450 q^{32} + 23830 q^{33} + 13228 q^{34} - 15856 q^{35} - 8040 q^{36} - 5842 q^{37} + 23276 q^{38} + 24662 q^{39} + 22886 q^{40} + 18706 q^{41} - 53596 q^{42} - 1922 q^{43} - 8006 q^{44} - 490 q^{45} - 19992 q^{46} + 38050 q^{47} + 16654 q^{48} + 48883 q^{49} + 2174 q^{50} + 36636 q^{51} - 63364 q^{52} - 49784 q^{53} + 4216 q^{54} - 78226 q^{55} - 45256 q^{56} - 39596 q^{57} + 3364 q^{58} + 2048 q^{59} - 155622 q^{60} + 152314 q^{61} - 24136 q^{62} - 61144 q^{63} - 30904 q^{64} - 51370 q^{65} - 40034 q^{66} + 95156 q^{67} + 105824 q^{68} - 48452 q^{69} + 271984 q^{70} - 100340 q^{71} + 143656 q^{72} - 92558 q^{73} - 23788 q^{74} - 51092 q^{75} + 219948 q^{76} + 34552 q^{77} + 49368 q^{78} + 105982 q^{79} + 201148 q^{80} - 187977 q^{81} - 32208 q^{82} - 60040 q^{83} - 72160 q^{84} - 85488 q^{85} - 279304 q^{86} + 45414 q^{87} + 97240 q^{88} + 41058 q^{89} + 97636 q^{90} - 74528 q^{91} - 136376 q^{92} - 252814 q^{93} + 469468 q^{94} + 15676 q^{95} - 195624 q^{96} - 167702 q^{97} + 213172 q^{98} + 467388 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(29))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 29
29.6.a.a 29.a 1.a $4$ $4.651$ 4.4.3257317.1 None \(0\) \(-28\) \(-68\) \(-208\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+(2-3\beta _{1}+\cdots)q^{4}+\cdots\)
29.6.a.b 29.a 1.a $7$ $4.651$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(26\) \(32\) \(184\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(4+\beta _{5})q^{3}+(23-3\beta _{1}+\cdots)q^{4}+\cdots\)