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Properties

Label 29.4.a
Level $29$
Weight $4$
Character orbit 29.a
Rep. character $\chi_{29}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $2$
Sturm bound $10$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(29))\).

Total New Old
Modular forms 9 7 2
Cusp forms 7 7 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
\(+\)\(5\)
\(-\)\(2\)

Trace form

\( 7 q - 2 q^{2} - 2 q^{3} + 16 q^{4} + 32 q^{6} + 24 q^{7} - 66 q^{8} + 65 q^{9} + O(q^{10}) \) \( 7 q - 2 q^{2} - 2 q^{3} + 16 q^{4} + 32 q^{6} + 24 q^{7} - 66 q^{8} + 65 q^{9} - 38 q^{10} - 14 q^{11} - 150 q^{12} - 12 q^{13} - 136 q^{14} - 72 q^{15} + 164 q^{16} + 126 q^{17} - 20 q^{18} - 6 q^{19} + 24 q^{20} - 40 q^{21} - 220 q^{22} + 216 q^{23} + 356 q^{24} + 71 q^{25} - 22 q^{26} + 112 q^{27} + 540 q^{28} - 87 q^{29} - 256 q^{30} + 126 q^{31} - 670 q^{32} - 2 q^{33} + 216 q^{34} + 188 q^{35} - 660 q^{36} + 690 q^{37} - 148 q^{38} + 68 q^{39} - 346 q^{40} - 1118 q^{41} + 284 q^{42} - 526 q^{43} + 1210 q^{44} - 1186 q^{45} + 720 q^{46} + 118 q^{47} - 2402 q^{48} - 441 q^{49} + 884 q^{50} - 288 q^{51} + 1820 q^{52} + 448 q^{53} + 700 q^{54} + 84 q^{55} - 1192 q^{56} + 760 q^{57} - 58 q^{58} - 460 q^{59} + 666 q^{60} - 330 q^{61} + 1292 q^{62} + 1748 q^{63} + 2712 q^{64} - 1942 q^{65} + 3262 q^{66} + 1484 q^{67} - 88 q^{68} - 2804 q^{69} - 2752 q^{70} - 1352 q^{71} - 3680 q^{72} - 1302 q^{73} - 2368 q^{74} + 4234 q^{75} + 2220 q^{76} - 2888 q^{77} - 1068 q^{78} + 530 q^{79} - 404 q^{80} + 3591 q^{81} + 604 q^{82} + 1724 q^{83} - 2800 q^{84} - 1640 q^{85} + 3452 q^{86} - 522 q^{87} - 5560 q^{88} + 1626 q^{89} - 2864 q^{90} + 1748 q^{91} + 2824 q^{92} + 2186 q^{93} - 6640 q^{94} + 3856 q^{95} + 6744 q^{96} + 1586 q^{97} - 3890 q^{98} - 5094 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(29))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 29
29.4.a.a 29.a 1.a $2$ $1.711$ \(\Q(\sqrt{2}) \) None 29.4.a.a \(-2\) \(-10\) \(-10\) \(-16\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(-5-3\beta )q^{3}+(-5+\cdots)q^{4}+\cdots\)
29.4.a.b 29.a 1.a $5$ $1.711$ 5.5.13458092.1 None 29.4.a.b \(0\) \(8\) \(10\) \(40\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(6+\cdots)q^{4}+\cdots\)