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Properties

Label 10.14
Level 10
Weight 14
Dimension 9
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 84
Trace bound 1

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(84\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(10))\).

Total New Old
Modular forms 43 9 34
Cusp forms 35 9 26
Eisenstein series 8 0 8

Trace form

\( 9 q - 64 q^{2} - 1196 q^{3} - 12288 q^{4} - 18095 q^{5} - 253184 q^{6} + 911448 q^{7} - 262144 q^{8} + 6708041 q^{9} + O(q^{10}) \) \( 9 q - 64 q^{2} - 1196 q^{3} - 12288 q^{4} - 18095 q^{5} - 253184 q^{6} + 911448 q^{7} - 262144 q^{8} + 6708041 q^{9} - 3269440 q^{10} + 2498188 q^{11} - 4898816 q^{12} + 11061714 q^{13} - 3464704 q^{14} + 137066260 q^{15} + 150994944 q^{16} - 103453482 q^{17} + 372909248 q^{18} + 322225380 q^{19} - 53882880 q^{20} - 2069045552 q^{21} - 322629888 q^{22} + 1421024184 q^{23} - 846200832 q^{24} + 2553329025 q^{25} - 3737508224 q^{26} - 8073208520 q^{27} + 3733291008 q^{28} + 6030959790 q^{29} + 7635083520 q^{30} - 32574809472 q^{31} - 1073741824 q^{32} + 13045553568 q^{33} + 31305058176 q^{34} + 24631453880 q^{35} - 7429337088 q^{36} - 11918863782 q^{37} - 19679601920 q^{38} + 114723735512 q^{39} + 5199626240 q^{40} - 69420278702 q^{41} - 61122725888 q^{42} - 72359820996 q^{43} + 4713857024 q^{44} + 71057726985 q^{45} + 4556583936 q^{46} - 26863031952 q^{47} - 20065550336 q^{48} + 52975627989 q^{49} + 17420516800 q^{50} - 232717661752 q^{51} + 45308780544 q^{52} - 157653331926 q^{53} - 158258588160 q^{54} - 262106071140 q^{55} - 4265607168 q^{56} + 243071852720 q^{57} - 29927779200 q^{58} + 72936532780 q^{59} - 94991400960 q^{60} + 1770976834038 q^{61} - 179690490368 q^{62} + 960503067464 q^{63} - 206158430208 q^{64} + 359648760010 q^{65} + 1086926451712 q^{66} + 1505490049428 q^{67} - 423745462272 q^{68} - 4338635621888 q^{69} - 1158953354240 q^{70} - 1396265571192 q^{71} + 1527436279808 q^{72} - 3774323316546 q^{73} + 4651700686976 q^{74} - 1787690724700 q^{75} + 151605166080 q^{76} - 3340375849584 q^{77} - 2971950685184 q^{78} + 3862418346000 q^{79} - 303583723520 q^{80} + 5550515178609 q^{81} - 726354265728 q^{82} - 5235628697196 q^{83} - 886069395456 q^{84} + 10449263851230 q^{85} - 7801318604544 q^{86} - 3099118014600 q^{87} - 1321492021248 q^{88} + 14631544796330 q^{89} - 6746657801280 q^{90} - 23416403106672 q^{91} + 5820515057664 q^{92} + 15413415130448 q^{93} + 31171175095296 q^{94} + 26502079886500 q^{95} - 4247722655744 q^{96} - 16569894091242 q^{97} - 347896646208 q^{98} - 12778089837268 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.14.a \(\chi_{10}(1, \cdot)\) 10.14.a.a 1 1
10.14.a.b 1
10.14.a.c 1
10.14.b \(\chi_{10}(9, \cdot)\) 10.14.b.a 6 1

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)