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Properties

Label 29.10.a
Level $29$
Weight $10$
Character orbit 29.a
Rep. character $\chi_{29}(1,\cdot)$
Character field $\Q$
Dimension $21$
Newform subspaces $2$
Sturm bound $25$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(25\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(29))\).

Total New Old
Modular forms 23 21 2
Cusp forms 21 21 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
\(+\)\(9\)
\(-\)\(12\)

Trace form

\( 21 q + 16 q^{2} - 2 q^{3} + 4692 q^{4} + 1024 q^{5} + 3116 q^{6} + 4952 q^{7} + 11574 q^{8} + 76043 q^{9} + O(q^{10}) \) \( 21 q + 16 q^{2} - 2 q^{3} + 4692 q^{4} + 1024 q^{5} + 3116 q^{6} + 4952 q^{7} + 11574 q^{8} + 76043 q^{9} - 8866 q^{10} - 35038 q^{11} - 141558 q^{12} - 58036 q^{13} + 271688 q^{14} - 187752 q^{15} + 611924 q^{16} + 587306 q^{17} + 687526 q^{18} - 172246 q^{19} + 2451832 q^{20} + 1161176 q^{21} - 2586488 q^{22} + 1304504 q^{23} + 3446852 q^{24} + 5356061 q^{25} + 2598958 q^{26} + 893056 q^{27} - 3374692 q^{28} + 2121843 q^{29} - 5983228 q^{30} + 5942846 q^{31} + 3776754 q^{32} + 889810 q^{33} + 24318612 q^{34} - 25527636 q^{35} - 5351448 q^{36} + 14907878 q^{37} - 53955540 q^{38} + 11626820 q^{39} - 16456154 q^{40} - 16544602 q^{41} - 47500876 q^{42} + 27199074 q^{43} + 12553242 q^{44} - 2439430 q^{45} - 56189832 q^{46} - 4135114 q^{47} + 23862478 q^{48} + 46286373 q^{49} - 125376046 q^{50} - 27304176 q^{51} - 20287524 q^{52} - 109140304 q^{53} - 95488832 q^{54} - 90653676 q^{55} + 186788600 q^{56} + 154793416 q^{57} + 11316496 q^{58} - 184555148 q^{59} - 155903622 q^{60} + 10050242 q^{61} + 263764288 q^{62} + 244693748 q^{63} + 126917992 q^{64} - 324226330 q^{65} + 529148734 q^{66} + 68999772 q^{67} + 439923168 q^{68} + 774790900 q^{69} + 300437584 q^{70} + 12858168 q^{71} + 224216488 q^{72} + 1007561198 q^{73} - 740828068 q^{74} - 450826262 q^{75} - 806187700 q^{76} + 224102840 q^{77} - 316242576 q^{78} + 230033490 q^{79} + 122335068 q^{80} - 707379867 q^{81} - 524405608 q^{82} + 1056186940 q^{83} - 1239468160 q^{84} - 659228968 q^{85} - 1963368576 q^{86} + 343738566 q^{87} - 1970782952 q^{88} + 15122734 q^{89} + 1605447916 q^{90} + 1579042148 q^{91} + 233364328 q^{92} - 588300082 q^{93} - 1968237788 q^{94} + 305625456 q^{95} + 1663591704 q^{96} + 2665131030 q^{97} - 164581184 q^{98} + 2429061930 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(29))\) 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
29.10.a.a 29.a 1.a $9$ $14.936$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-244\) \(-738\) \(-7128\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-3^{3}-\beta _{4})q^{3}+(133+2\beta _{1}+\cdots)q^{4}+\cdots\)
29.10.a.b 29.a 1.a $12$ $14.936$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(16\) \(242\) \(1762\) \(12080\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(20+\beta _{1}-\beta _{3})q^{3}+(291+\cdots)q^{4}+\cdots\)