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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 29
29.4.a.a \(2\) \(1.711\) \(\Q(\sqrt{2}) \) None \(-2\) \(-10\) \(-10\) \(-16\) \(-\) \(q+(-1+\beta )q^{2}+(-5-3\beta )q^{3}+(-5+\cdots)q^{4}+\cdots\)
29.4.a.b \(5\) \(1.711\) 5.5.13458092.1 None \(0\) \(8\) \(10\) \(40\) \(+\) \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+(6+\cdots)q^{4}+\cdots\)