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Properties

Label 14.16
Level 14
Weight 16
Dimension 28
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 192
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(192\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(14))\).

Total New Old
Modular forms 96 28 68
Cusp forms 84 28 56
Eisenstein series 12 0 12

Trace form

\( 28 q + 256 q^{2} - 3756 q^{3} - 32768 q^{4} + 285996 q^{5} - 79104 q^{6} + 6429592 q^{7} + 4194304 q^{8} - 47565984 q^{9} + O(q^{10}) \) \( 28 q + 256 q^{2} - 3756 q^{3} - 32768 q^{4} + 285996 q^{5} - 79104 q^{6} + 6429592 q^{7} + 4194304 q^{8} - 47565984 q^{9} + 74524416 q^{10} + 33436410 q^{11} - 61538304 q^{12} - 755035930 q^{13} - 192649472 q^{14} + 1600194228 q^{15} - 536870912 q^{16} - 4080005850 q^{17} + 13212307200 q^{18} - 9141926860 q^{19} - 10645831680 q^{20} + 25282853328 q^{21} + 5988020736 q^{22} - 2758427574 q^{23} - 3913285632 q^{24} + 120714270220 q^{25} + 59389229312 q^{26} - 259366107312 q^{27} + 51658719232 q^{28} + 166923506772 q^{29} - 176941857792 q^{30} - 27407735590 q^{31} + 68719476736 q^{32} + 600762731118 q^{33} - 977368691712 q^{34} - 254178109500 q^{35} + 2310986072064 q^{36} + 149501070998 q^{37} + 680733350144 q^{38} - 5160046935828 q^{39} + 1221008031744 q^{40} + 774096412212 q^{41} + 2636743236864 q^{42} - 7608084350236 q^{43} + 547822141440 q^{44} + 8191933970142 q^{45} + 6517917729792 q^{46} - 22499484843930 q^{47} - 4530653626368 q^{48} - 1054043593700 q^{49} + 19770420630784 q^{50} + 4877277256998 q^{51} - 2461611163648 q^{52} + 16890448302834 q^{53} + 10438917788160 q^{54} - 82843153534188 q^{55} + 6975391793152 q^{56} - 888707475096 q^{57} + 37836850510848 q^{58} + 34826010431712 q^{59} - 19996244803584 q^{60} + 17764201919300 q^{61} + 49843200430592 q^{62} - 249097382788008 q^{63} + 123145302310912 q^{64} + 282008770328544 q^{65} + 102986333460480 q^{66} + 51589501420622 q^{67} - 66846815846400 q^{68} - 382281948276804 q^{69} - 195442965532416 q^{70} - 139102867007928 q^{71} + 216470441164800 q^{72} + 795700735942514 q^{73} - 50714292542464 q^{74} - 715692370365006 q^{75} - 272006879543296 q^{76} - 417658274857614 q^{77} + 37599291531264 q^{78} + 878030081386874 q^{79} + 76771466674176 q^{80} + 929178184777770 q^{81} - 842153458771968 q^{82} - 2321219092488174 q^{83} - 471920575315968 q^{84} + 1894789332089160 q^{85} + 566915957886464 q^{86} + 3615368443152696 q^{87} + 208807762329600 q^{88} - 1635224180138790 q^{89} - 4239571384073472 q^{90} - 3013237483489510 q^{91} + 1026855547502592 q^{92} + 5138898435555006 q^{93} + 2093972251614720 q^{94} - 832725641566938 q^{95} - 64115271794688 q^{96} - 5168668714908820 q^{97} - 2045051439820544 q^{98} + 1427989031154660 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.16.a \(\chi_{14}(1, \cdot)\) 14.16.a.a 1 1
14.16.a.b 2
14.16.a.c 2
14.16.a.d 3
14.16.c \(\chi_{14}(9, \cdot)\) 14.16.c.a 10 2
14.16.c.b 10

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)