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Properties

Label 129.8
Level 129
Weight 8
Dimension 3190
Nonzero newspaces 8
Sturm bound 9856
Trace bound 1

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Defining parameters

Level: \( N \) = \( 129 = 3 \cdot 43 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(9856\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(129))\).

Total New Old
Modular forms 4396 3274 1122
Cusp forms 4228 3190 1038
Eisenstein series 168 84 84

Trace form

\( 3190 q - 12 q^{2} + 33 q^{3} + 142 q^{4} - 780 q^{5} + 303 q^{6} + 86 q^{7} + 2640 q^{8} - 1479 q^{9} + O(q^{10}) \) \( 3190 q - 12 q^{2} + 33 q^{3} + 142 q^{4} - 780 q^{5} + 303 q^{6} + 86 q^{7} + 2640 q^{8} - 1479 q^{9} - 4722 q^{10} + 1896 q^{11} - 4989 q^{12} + 10154 q^{13} + 768 q^{14} + 21039 q^{15} - 7754 q^{16} - 56772 q^{17} - 8769 q^{18} + 17198 q^{19} + 71760 q^{20} - 3477 q^{21} + 11334 q^{22} + 30576 q^{23} - 71301 q^{24} - 147992 q^{25} + 61176 q^{26} + 39345 q^{27} - 11818 q^{28} - 73020 q^{29} + 126339 q^{30} + 2934988 q^{31} - 1927104 q^{32} - 2479107 q^{33} - 4067250 q^{34} + 1288836 q^{35} + 1440483 q^{36} + 4057454 q^{37} + 6690384 q^{38} + 104388 q^{39} - 8625738 q^{40} - 1220202 q^{41} - 6244128 q^{42} - 15097484 q^{43} - 7260000 q^{44} - 538023 q^{45} + 8754102 q^{46} + 2877042 q^{47} + 20819787 q^{48} + 13168454 q^{49} + 11400492 q^{50} + 1105305 q^{51} - 27416666 q^{52} - 17443032 q^{53} + 236175 q^{54} - 9885846 q^{55} + 23802624 q^{56} + 7678698 q^{57} - 438162 q^{58} - 2612760 q^{59} - 1937541 q^{60} - 601366 q^{61} + 3321696 q^{62} + 93291 q^{63} - 1318058 q^{64} + 3976440 q^{65} - 307173 q^{66} + 1014446 q^{67} + 5223024 q^{68} + 47545113 q^{69} - 9129522 q^{70} - 56299740 q^{71} - 118158291 q^{72} - 33601234 q^{73} - 25347870 q^{74} + 33854004 q^{75} + 117901652 q^{76} + 127236180 q^{77} + 133593246 q^{78} + 79305902 q^{79} + 68770320 q^{80} - 1259295 q^{81} - 85159686 q^{82} - 60635040 q^{83} - 207882243 q^{84} - 125314080 q^{85} - 203063256 q^{86} - 99614532 q^{87} - 102694938 q^{88} + 7921284 q^{89} + 79890009 q^{90} + 82020382 q^{91} + 300812148 q^{92} + 131945331 q^{93} + 299258694 q^{94} + 142404600 q^{95} + 160512516 q^{96} + 54376790 q^{97} - 99186834 q^{98} - 135431766 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(129))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
129.8.a \(\chi_{129}(1, \cdot)\) 129.8.a.a 10 1
129.8.a.b 12
129.8.a.c 13
129.8.a.d 15
129.8.d \(\chi_{129}(128, \cdot)\) 129.8.d.a 100 1
129.8.e \(\chi_{129}(49, \cdot)\) n/a 102 2
129.8.h \(\chi_{129}(50, \cdot)\) n/a 202 2
129.8.i \(\chi_{129}(4, \cdot)\) n/a 312 6
129.8.j \(\chi_{129}(2, \cdot)\) n/a 600 6
129.8.m \(\chi_{129}(10, \cdot)\) n/a 612 12
129.8.n \(\chi_{129}(5, \cdot)\) n/a 1212 12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(129))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(129)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 2}\)