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Properties

Label 5.19
Level 5
Weight 19
Dimension 16
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 38
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 19 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(38\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(\Gamma_1(5))\).

Total New Old
Modular forms 20 20 0
Cusp forms 16 16 0
Eisenstein series 4 4 0

Trace form

\( 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8} + O(q^{10}) \) \( 16 q + 510 q^{2} - 20130 q^{3} + 3145170 q^{5} - 30766728 q^{6} + 78767350 q^{7} - 217339260 q^{8} - 635093930 q^{10} + 4719921012 q^{11} - 22715951880 q^{12} + 8689116940 q^{13} - 59706310410 q^{15} + 10530345976 q^{16} - 221748184620 q^{17} + 654304109970 q^{18} - 878373508140 q^{20} + 1431507507492 q^{21} + 2209421844320 q^{22} - 3507966822690 q^{23} + 10464353188900 q^{25} - 23324455191468 q^{26} + 11679867134280 q^{27} + 8077754165240 q^{28} - 80865025845360 q^{30} + 53033402941772 q^{31} + 20394786468360 q^{32} - 4953707733660 q^{33} - 82375887392730 q^{35} + 263454471040956 q^{36} - 29247362581160 q^{37} + 391580910829560 q^{38} - 918259855204500 q^{40} - 717170436410748 q^{41} + 1119760897992480 q^{42} + 1295649718427950 q^{43} - 2413910465914410 q^{45} - 6165422784262408 q^{46} + 5324712362382270 q^{47} + 7675815427929360 q^{48} - 10266398091964350 q^{50} - 5996743906200468 q^{51} + 5457051468349900 q^{52} + 25019175284457720 q^{53} - 28447209909214060 q^{55} - 22879869030140400 q^{56} + 26327201869272960 q^{57} + 72036625362175440 q^{58} - 129993967558538280 q^{60} - 55112667981951388 q^{61} + 98952816959518920 q^{62} + 129200567352114030 q^{63} - 145786436727900960 q^{65} - 217789774433419296 q^{66} + 132604737823930030 q^{67} + 291394918710173220 q^{68} - 344767752141139080 q^{70} - 148288220084109108 q^{71} + 428373837658219140 q^{72} + 357896091854250160 q^{73} - 656924515001553450 q^{75} - 254554257141486000 q^{76} + 201286979542193700 q^{77} + 866949362074211400 q^{78} - 608571216720410880 q^{80} - 330578957555881164 q^{81} - 167911799138733280 q^{82} + 314012877447835830 q^{83} - 37755360901186580 q^{85} - 149686440788368488 q^{86} + 359090097519437040 q^{87} - 966828856938988320 q^{88} + 2368537241357586390 q^{90} + 498102030062089052 q^{91} - 1299658879961370120 q^{92} - 3025937916654554460 q^{93} + 2986575636848949000 q^{95} + 3531977749160666592 q^{96} - 1689002222572272080 q^{97} - 4330619740553781090 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{19}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.19.c \(\chi_{5}(2, \cdot)\) 5.19.c.a 16 2