Properties

Label 29.6.d
Level $29$
Weight $6$
Character orbit 29.d
Rep. character $\chi_{29}(7,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $66$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 29.d (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(29, [\chi])\).

Total New Old
Modular forms 78 78 0
Cusp forms 66 66 0
Eisenstein series 12 12 0

Trace form

\( 66 q - 11 q^{2} - 5 q^{3} - 171 q^{4} + 29 q^{5} + 445 q^{6} + 17 q^{7} + 1046 q^{8} - 732 q^{9} + O(q^{10}) \) \( 66 q - 11 q^{2} - 5 q^{3} - 171 q^{4} + 29 q^{5} + 445 q^{6} + 17 q^{7} + 1046 q^{8} - 732 q^{9} - 141 q^{10} + 1125 q^{11} - 248 q^{12} - 1789 q^{13} + 1233 q^{14} + 1061 q^{15} + 2629 q^{16} + 676 q^{17} - 10896 q^{18} - 1903 q^{19} + 4081 q^{20} - 439 q^{21} - 2980 q^{22} + 9945 q^{23} + 10741 q^{24} - 22114 q^{25} - 1641 q^{26} - 4427 q^{27} + 7508 q^{28} - 13100 q^{29} - 40018 q^{30} + 8541 q^{31} + 18996 q^{32} + 20725 q^{33} - 8839 q^{34} + 14127 q^{35} + 70172 q^{36} + 3791 q^{37} + 36322 q^{38} + 25843 q^{39} - 72621 q^{40} - 18720 q^{41} - 72614 q^{42} - 10419 q^{43} + 35796 q^{44} + 23163 q^{45} + 15848 q^{46} - 40549 q^{47} - 4194 q^{48} + 19808 q^{49} + 201932 q^{50} + 51998 q^{51} + 8330 q^{52} - 72275 q^{53} - 197108 q^{54} + 42183 q^{55} + 31599 q^{56} - 40162 q^{57} - 258031 q^{58} - 333512 q^{59} + 26920 q^{60} - 175281 q^{61} + 213745 q^{62} + 354423 q^{63} - 19790 q^{64} - 79593 q^{65} + 103783 q^{66} + 135179 q^{67} + 334644 q^{68} + 73673 q^{69} - 511678 q^{70} - 187563 q^{71} - 17551 q^{72} - 56675 q^{73} + 159980 q^{74} + 538208 q^{75} - 215041 q^{76} + 106099 q^{77} + 37481 q^{78} + 273775 q^{79} + 571652 q^{80} - 61356 q^{81} - 37092 q^{82} - 237831 q^{83} + 127523 q^{84} - 148844 q^{85} - 348400 q^{86} - 110493 q^{87} - 985638 q^{88} + 74239 q^{89} - 630714 q^{90} + 100309 q^{91} + 132694 q^{92} - 307921 q^{93} + 206074 q^{94} + 37965 q^{95} + 687094 q^{96} + 136055 q^{97} - 115704 q^{98} + 438608 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(29, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
29.6.d.a \(66\) \(4.651\) None \(-11\) \(-5\) \(29\) \(17\)