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Properties

Label 10.19
Level 10
Weight 19
Dimension 18
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 114
Trace bound 0

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 19 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(114\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(\Gamma_1(10))\).

Total New Old
Modular forms 58 18 40
Cusp forms 50 18 32
Eisenstein series 8 0 8

Trace form

\( 18 q - 512 q^{2} + 40256 q^{3} - 4568580 q^{5} + 17303552 q^{6} - 115408296 q^{7} + 67108864 q^{8} + O(q^{10}) \) \( 18 q - 512 q^{2} + 40256 q^{3} - 4568580 q^{5} + 17303552 q^{6} - 115408296 q^{7} + 67108864 q^{8} - 81676800 q^{10} - 7363140664 q^{11} + 5276434432 q^{12} - 25477516674 q^{13} + 87678834920 q^{15} - 309237645312 q^{16} + 188810525174 q^{17} - 95031950848 q^{18} + 270274396160 q^{20} + 80506547816 q^{21} + 513560088576 q^{22} + 582931021376 q^{23} - 4603213766250 q^{25} - 901355179008 q^{26} - 26508250069240 q^{27} + 15126796173312 q^{28} - 49017972817920 q^{30} + 2786268042576 q^{31} + 8796093022208 q^{32} - 87306279421288 q^{33} + 166344527736200 q^{35} + 273224567619584 q^{36} + 93401055588474 q^{37} - 174962309539840 q^{38} + 103132566650880 q^{40} + 761574180497576 q^{41} - 1310564670009344 q^{42} - 395922537735984 q^{43} + 663668107771630 q^{45} + 2766146448033792 q^{46} - 3966554842612896 q^{47} - 691592813871104 q^{48} + 5870531815846400 q^{50} + 5885354842608496 q^{51} - 3339389065494528 q^{52} - 20573443280907734 q^{53} + 34958696853916440 q^{55} - 1895742461444096 q^{56} - 28354034337743920 q^{57} - 13743553622814720 q^{58} + 7360706615705600 q^{60} + 70737232382913816 q^{61} - 21854083917277184 q^{62} - 176014195725647584 q^{63} + 188858801951429970 q^{65} + 48512069647253504 q^{66} - 151516283122082016 q^{67} - 24747773155606528 q^{68} + 100145176859105280 q^{70} + 173697306329185456 q^{71} - 12456027861549056 q^{72} - 319671145587769614 q^{73} + 507802869557246200 q^{75} + 184867243001118720 q^{76} + 21805515205557208 q^{77} - 588803221054580736 q^{78} + 78487606756638720 q^{80} - 305585914779798602 q^{81} + 80786352533999616 q^{82} + 133104235053833976 q^{83} + 218382571237434750 q^{85} + 487564692412803072 q^{86} - 1549659042362815360 q^{87} - 67313347929833472 q^{88} - 1139888554221160960 q^{90} + 990675121051799136 q^{91} + 76405934833795072 q^{92} + 1961172700046119592 q^{93} - 2589032345267576600 q^{95} - 297272759778541568 q^{96} + 2758556690180248914 q^{97} + 2898032974867639808 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{19}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.19.c \(\chi_{10}(3, \cdot)\) 10.19.c.a 8 2
10.19.c.b 10

Decomposition of \(S_{19}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{19}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{19}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)