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Properties

Label 10.15
Level 10
Weight 15
Dimension 14
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 90
Trace bound 0

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(10))\).

Total New Old
Modular forms 46 14 32
Cusp forms 38 14 24
Eisenstein series 8 0 8

Trace form

\( 14 q + 128 q^{2} + 4316 q^{3} - 18360 q^{5} - 193024 q^{6} + 2276404 q^{7} - 1048576 q^{8} + O(q^{10}) \) \( 14 q + 128 q^{2} + 4316 q^{3} - 18360 q^{5} - 193024 q^{6} + 2276404 q^{7} - 1048576 q^{8} - 7162240 q^{10} - 37385312 q^{11} + 35356672 q^{12} - 62678454 q^{13} + 274242020 q^{15} - 939524096 q^{16} - 1964204366 q^{17} + 1747732352 q^{18} - 1245593600 q^{20} + 2430032288 q^{21} + 3439860736 q^{22} - 14210081444 q^{23} + 20093156050 q^{25} + 5327383296 q^{26} - 8204936440 q^{27} - 18648301568 q^{28} + 81534197760 q^{30} + 39509750408 q^{31} - 8589934592 q^{32} - 178484453008 q^{33} + 251196204580 q^{35} + 308526989312 q^{36} - 461352680346 q^{37} - 344970544640 q^{38} + 133593825280 q^{40} + 139879775968 q^{41} - 130879407104 q^{42} - 1877928676884 q^{43} + 3457530818350 q^{45} + 595487407616 q^{46} - 2764042756356 q^{47} - 289641857024 q^{48} - 298566300800 q^{50} + 3877652640808 q^{51} - 513461895168 q^{52} - 1327743828874 q^{53} + 1729820852880 q^{55} - 409099829248 q^{56} + 6351081117680 q^{57} - 3114146821120 q^{58} - 285246914560 q^{60} - 17802895306512 q^{61} + 2052284135936 q^{62} + 21156226959836 q^{63} - 12397589330130 q^{65} - 10487613534208 q^{66} + 5072888673244 q^{67} + 16090762166272 q^{68} - 33059949299200 q^{70} - 29207869342552 q^{71} + 14317423427584 q^{72} + 37389431247566 q^{73} - 55690527253100 q^{75} + 18396758343680 q^{76} + 78627263681648 q^{77} + 46592717781504 q^{78} + 1232118743040 q^{80} - 182249102406926 q^{81} + 3105130249216 q^{82} + 73751207807316 q^{83} + 81462318897130 q^{85} - 895690258944 q^{86} + 13968334823840 q^{87} - 28179339149312 q^{88} + 103532852301440 q^{90} + 168032450337048 q^{91} - 116408987189248 q^{92} - 223291343115808 q^{93} - 7653238312600 q^{95} + 12953621364736 q^{96} - 139856069255346 q^{97} + 65145530885248 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(10))\)

We only show spaces with odd 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
10.15.c \(\chi_{10}(3, \cdot)\) 10.15.c.a 6 2
10.15.c.b 8

Decomposition of \(S_{15}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{15}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{15}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)