Properties

Label 19.12
Level 19
Weight 12
Dimension 154
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 360
Trace bound 1

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Defining parameters

Level: \( N \) = \( 19 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(360\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(19))\).

Total New Old
Modular forms 174 170 4
Cusp forms 156 154 2
Eisenstein series 18 16 2

Trace form

\( 154 q + 39 q^{2} - 513 q^{3} + 2935 q^{4} - 9669 q^{5} + 12087 q^{6} + 33479 q^{7} - 168969 q^{8} + 227277 q^{9} + O(q^{10}) \) \( 154 q + 39 q^{2} - 513 q^{3} + 2935 q^{4} - 9669 q^{5} + 12087 q^{6} + 33479 q^{7} - 168969 q^{8} + 227277 q^{9} + 231831 q^{10} - 1069233 q^{11} + 3727863 q^{12} - 2201017 q^{13} + 10614327 q^{14} - 7346331 q^{15} - 38432777 q^{16} + 16791372 q^{17} + 45563454 q^{18} + 5118202 q^{19} - 79083282 q^{20} - 70029864 q^{21} + 46095831 q^{22} + 28461534 q^{23} + 163454967 q^{24} - 102890741 q^{25} - 331123881 q^{26} + 266881698 q^{27} + 433799360 q^{28} - 795498027 q^{29} + 509580594 q^{30} + 717229325 q^{31} + 927688914 q^{32} - 1887810579 q^{33} - 2365068636 q^{34} - 400616493 q^{35} + 2983620357 q^{36} + 1612617836 q^{37} + 3395703162 q^{38} - 680842800 q^{39} - 6619421448 q^{40} - 2676351675 q^{41} - 4646658303 q^{42} - 354428692 q^{43} + 20535696822 q^{44} + 6662345328 q^{45} - 11126818872 q^{46} - 11032113606 q^{47} - 3919380768 q^{48} + 12534855036 q^{49} + 22140136146 q^{50} - 20899661859 q^{51} - 27786054409 q^{52} - 6859805265 q^{53} - 1787781276 q^{54} + 8219149155 q^{55} + 62308098030 q^{56} + 17551772316 q^{57} + 9069943950 q^{58} - 7905061074 q^{59} - 100057032630 q^{60} + 10893307133 q^{61} - 46531349760 q^{62} - 64392903981 q^{63} + 15886165231 q^{64} + 104810177226 q^{65} + 174023112447 q^{66} + 109004479142 q^{67} - 128836601532 q^{68} - 143016426882 q^{69} - 200677711725 q^{70} + 16042645800 q^{71} + 7790307984 q^{72} - 11282599621 q^{73} + 119646890079 q^{74} + 212187546882 q^{75} + 200220236821 q^{76} + 57319621125 q^{77} + 157550061033 q^{78} - 282813704863 q^{79} - 509571363729 q^{80} - 406079502786 q^{81} - 189902100330 q^{82} + 191860325724 q^{83} + 941968301499 q^{84} + 589829563035 q^{85} + 316648282434 q^{86} - 165695794857 q^{87} - 826911971793 q^{88} - 541641417372 q^{89} - 974879270694 q^{90} - 86207693261 q^{91} + 783287154870 q^{92} + 903890176317 q^{93} - 402687005886 q^{94} + 799549576440 q^{95} + 1232129613222 q^{96} - 460738482238 q^{97} - 1862886789054 q^{98} - 1105640405856 q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(19))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
19.12.a \(\chi_{19}(1, \cdot)\) 19.12.a.a 7 1
19.12.a.b 9
19.12.c \(\chi_{19}(7, \cdot)\) 19.12.c.a 36 2
19.12.e \(\chi_{19}(4, \cdot)\) 19.12.e.a 102 6

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(19))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(19)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)