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Properties

Label 8.16
Level 8
Weight 16
Dimension 18
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 64
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(64\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(8))\).

Total New Old
Modular forms 33 20 13
Cusp forms 27 18 9
Eisenstein series 6 2 4

Trace form

\( 18 q - 90 q^{2} - 4816 q^{3} + 51444 q^{4} - 78792 q^{5} - 189428 q^{6} - 2471440 q^{7} + 1889640 q^{8} - 39835930 q^{9} + O(q^{10}) \) \( 18 q - 90 q^{2} - 4816 q^{3} + 51444 q^{4} - 78792 q^{5} - 189428 q^{6} - 2471440 q^{7} + 1889640 q^{8} - 39835930 q^{9} + 58467784 q^{10} - 77853168 q^{11} + 399357832 q^{12} + 66385432 q^{13} - 518960496 q^{14} + 948886320 q^{15} - 1435931120 q^{16} + 1074989316 q^{17} + 526853306 q^{18} - 5038000912 q^{19} - 3449250768 q^{20} + 15735268992 q^{21} + 28367364252 q^{22} - 77874357552 q^{23} + 40155187088 q^{24} + 35085600370 q^{25} + 17666210712 q^{26} - 190050794272 q^{27} + 79863955680 q^{28} + 209796530136 q^{29} - 124878825712 q^{30} - 482821783104 q^{31} - 37651613280 q^{32} + 703153747160 q^{33} + 537472307308 q^{34} - 929457797568 q^{35} + 338679650892 q^{36} + 603580348344 q^{37} + 1649727781164 q^{38} - 3650772379824 q^{39} + 1251083710304 q^{40} + 1357934223060 q^{41} - 2437011096800 q^{42} + 2916482940304 q^{43} - 3416842360344 q^{44} - 7867578801128 q^{45} - 3303531082064 q^{46} + 22583752082592 q^{47} - 6441543679584 q^{48} - 2878124879710 q^{49} + 1179755527374 q^{50} + 10407251548000 q^{51} - 2436018627056 q^{52} - 14453600213640 q^{53} + 3357642572216 q^{54} - 8814114837968 q^{55} + 7549064859072 q^{56} + 8508811648248 q^{57} - 8014960165320 q^{58} - 5476736925360 q^{59} - 53574657402912 q^{60} + 11293162832728 q^{61} + 77882578979904 q^{62} + 16523547823696 q^{63} + 76083381630528 q^{64} + 21238662295536 q^{65} - 134116957601160 q^{66} - 101238902133712 q^{67} - 69772560247896 q^{68} + 215730284047232 q^{69} + 133952399750848 q^{70} - 261021648050832 q^{71} + 163390222317848 q^{72} - 71020551968108 q^{73} + 2072780135688 q^{74} - 405206000663216 q^{75} - 248503439494072 q^{76} + 144267440340864 q^{77} + 636498768647600 q^{78} - 123019488416160 q^{79} + 766230078246336 q^{80} + 392603178462234 q^{81} - 1021513680215332 q^{82} - 33861880122384 q^{83} - 1701668269684544 q^{84} - 686208914866960 q^{85} + 1418597672590812 q^{86} + 2833455945027984 q^{87} + 1948789255860816 q^{88} - 632035288029324 q^{89} - 3574690367103304 q^{90} - 146193789167808 q^{91} - 3044080509008736 q^{92} - 1147797513827840 q^{93} + 3407319354561120 q^{94} + 1923759757359408 q^{95} + 4705878559349312 q^{96} - 749552317045916 q^{97} - 5140373067292458 q^{98} - 2625158795769776 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.16.a \(\chi_{8}(1, \cdot)\) 8.16.a.a 1 1
8.16.a.b 1
8.16.a.c 2
8.16.b \(\chi_{8}(5, \cdot)\) 8.16.b.a 14 1

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)