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Properties

Label 100.14
Level 100
Weight 14
Dimension 2074
Nonzero newspaces 6
Sturm bound 8400
Trace bound 3

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Defining parameters

Level: \( N \) = \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(8400\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(100))\).

Total New Old
Modular forms 3970 2114 1856
Cusp forms 3830 2074 1756
Eisenstein series 140 40 100

Trace form

\( 2074 q - 6 q^{2} - 1928 q^{3} - 10 q^{4} - 22535 q^{5} + 309086 q^{6} + 17188 q^{7} + 2153742 q^{8} + 780999 q^{9} + O(q^{10}) \) \( 2074 q - 6 q^{2} - 1928 q^{3} - 10 q^{4} - 22535 q^{5} + 309086 q^{6} + 17188 q^{7} + 2153742 q^{8} + 780999 q^{9} + 3836864 q^{10} + 19151260 q^{11} - 41083530 q^{12} - 57139038 q^{13} - 10 q^{14} - 81881122 q^{15} + 3002494 q^{16} + 414307884 q^{17} + 27305042 q^{18} - 721595656 q^{19} - 60759926 q^{20} + 2159354512 q^{21} - 983522170 q^{22} - 701745256 q^{23} - 1644330477 q^{25} + 1404446332 q^{26} + 3840856306 q^{27} + 3832476470 q^{28} - 10776863286 q^{29} + 7202736030 q^{30} + 1457975540 q^{31} + 21927862374 q^{32} - 8353571160 q^{33} - 10 q^{34} + 27572273672 q^{35} - 50589063690 q^{36} + 41463622991 q^{37} + 61952708880 q^{38} + 140354932584 q^{39} - 136189033396 q^{40} + 20790705518 q^{41} - 110942896510 q^{42} + 234917700440 q^{43} + 167952706660 q^{44} - 282907626085 q^{45} - 12822461454 q^{46} - 247470670684 q^{47} + 514657001560 q^{48} + 600851012268 q^{49} + 458011215794 q^{50} - 268912346980 q^{51} - 460414431392 q^{52} - 1537993148425 q^{53} - 679686075780 q^{54} + 1139588230360 q^{55} - 1552147361014 q^{56} + 1229241835772 q^{57} + 1349751143024 q^{58} - 1927341461182 q^{59} - 2370157613590 q^{60} - 603772773482 q^{61} - 1933857908660 q^{62} + 4162036875658 q^{63} - 5899336531180 q^{64} + 2769660485995 q^{65} + 11382443640270 q^{66} - 2417102695992 q^{67} - 4675128973586 q^{68} - 3246349166978 q^{69} - 4488822537370 q^{70} + 3019419974360 q^{71} + 13163584637744 q^{72} - 4112479371378 q^{73} - 10620737178958 q^{75} - 7995111322140 q^{76} + 8181307516700 q^{77} + 14469787784420 q^{78} + 6447405618072 q^{79} + 369858859494 q^{80} + 26692123045031 q^{81} + 15212375268878 q^{82} - 8730705462186 q^{83} - 48620732507290 q^{84} + 21002315010627 q^{85} + 37943684877226 q^{86} - 6638558281418 q^{87} + 9445396657790 q^{88} - 2798464432229 q^{89} - 96089864742106 q^{90} + 4610654475100 q^{91} - 12620081111710 q^{92} - 35300620061078 q^{93} + 110723894347030 q^{94} + 10842376486996 q^{95} + 83780536177226 q^{96} - 9190836169414 q^{97} - 162713369293738 q^{98} - 86572639789720 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(100))\)

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
100.14.a \(\chi_{100}(1, \cdot)\) 100.14.a.a 1 1
100.14.a.b 2
100.14.a.c 3
100.14.a.d 4
100.14.a.e 4
100.14.a.f 6
100.14.c \(\chi_{100}(49, \cdot)\) 100.14.c.a 2 1
100.14.c.b 4
100.14.c.c 6
100.14.c.d 8
100.14.e \(\chi_{100}(7, \cdot)\) n/a 230 2
100.14.g \(\chi_{100}(21, \cdot)\) n/a 132 4
100.14.i \(\chi_{100}(9, \cdot)\) n/a 128 4
100.14.l \(\chi_{100}(3, \cdot)\) n/a 1544 8

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(100))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(100)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)