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Properties

Label 99.14
Level 99
Weight 14
Dimension 3602
Nonzero newspaces 8
Sturm bound 10080
Trace bound 2

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Defining parameters

Level: \( N \) = \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(10080\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(99))\).

Total New Old
Modular forms 4760 3682 1078
Cusp forms 4600 3602 998
Eisenstein series 160 80 80

Trace form

\( 3602 q - 273 q^{2} + 1444 q^{3} + 66251 q^{4} - 83259 q^{5} + 358846 q^{6} + 280244 q^{7} - 2562659 q^{8} - 495452 q^{9} + O(q^{10}) \) \( 3602 q - 273 q^{2} + 1444 q^{3} + 66251 q^{4} - 83259 q^{5} + 358846 q^{6} + 280244 q^{7} - 2562659 q^{8} - 495452 q^{9} - 1158738 q^{10} - 12424036 q^{11} - 6220528 q^{12} + 62060288 q^{13} - 153150726 q^{14} - 251356196 q^{15} + 746294591 q^{16} - 5623074 q^{17} - 605438300 q^{18} + 1166652616 q^{19} - 1322355140 q^{20} + 2358906940 q^{21} - 551602800 q^{22} - 3411072233 q^{23} - 4631798366 q^{24} - 8007926259 q^{25} + 7991853898 q^{26} + 18195372154 q^{27} + 15493180518 q^{28} - 52207433336 q^{29} + 15250270972 q^{30} + 48769453725 q^{31} + 33564396184 q^{32} + 997659330 q^{33} - 82987151156 q^{34} - 71661665392 q^{35} + 14445133574 q^{36} + 1209083537 q^{37} + 273348619792 q^{38} + 16601042650 q^{39} - 368506269754 q^{40} - 175537106628 q^{41} + 286465488904 q^{42} + 117285498716 q^{43} - 474666824096 q^{44} - 73084305486 q^{45} + 621701691442 q^{46} - 141065081194 q^{47} - 1156435062490 q^{48} - 372317663488 q^{49} + 701238935197 q^{50} + 1228237338758 q^{51} - 42981808324 q^{52} + 548365403726 q^{53} + 509585159274 q^{54} - 2930081658001 q^{55} - 3577295272200 q^{56} + 170263975236 q^{57} + 4905380098110 q^{58} + 457634989263 q^{59} - 1991705882016 q^{60} - 2453444672568 q^{61} - 3747711027948 q^{62} + 2842797260652 q^{63} + 4164690689795 q^{64} + 10253324041938 q^{65} + 6096610178384 q^{66} - 1929151216503 q^{67} - 25508728329166 q^{68} - 11285178880068 q^{69} - 13792960086522 q^{70} + 22257223442523 q^{71} + 34379041732348 q^{72} + 4173497591686 q^{73} + 8317348189896 q^{74} - 12331931312686 q^{75} - 37922795630974 q^{76} - 38755281211884 q^{77} - 16851588441864 q^{78} + 19900490208980 q^{79} + 106919019972834 q^{80} + 46186498964788 q^{81} - 15436985058499 q^{82} - 24408993220258 q^{83} - 93998263098386 q^{84} - 34842766516856 q^{85} - 22003503448361 q^{86} + 38950475977512 q^{87} + 16338903848854 q^{88} + 9279231899011 q^{89} + 2671495330964 q^{90} + 60665465810104 q^{91} + 37789456439152 q^{92} - 60306184263576 q^{93} - 109192651709796 q^{94} - 187557545658 q^{95} + 21317581261898 q^{96} + 27211226401549 q^{97} + 51483320740016 q^{98} - 58294299540492 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(99))\)

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
99.14.a \(\chi_{99}(1, \cdot)\) 99.14.a.a 1 1
99.14.a.b 4
99.14.a.c 4
99.14.a.d 5
99.14.a.e 5
99.14.a.f 6
99.14.a.g 7
99.14.a.h 11
99.14.a.i 11
99.14.d \(\chi_{99}(98, \cdot)\) 99.14.d.a 52 1
99.14.e \(\chi_{99}(34, \cdot)\) n/a 260 2
99.14.f \(\chi_{99}(37, \cdot)\) n/a 256 4
99.14.g \(\chi_{99}(32, \cdot)\) n/a 308 2
99.14.j \(\chi_{99}(8, \cdot)\) n/a 208 4
99.14.m \(\chi_{99}(4, \cdot)\) n/a 1232 8
99.14.p \(\chi_{99}(2, \cdot)\) n/a 1232 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(99))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(99)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)