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Properties

Label 16.14
Level 16
Weight 14
Dimension 56
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 224
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(224\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 111 61 50
Cusp forms 97 56 41
Eisenstein series 14 5 9

Trace form

\( 56 q - 2 q^{2} - 730 q^{3} + 360 q^{4} + 16898 q^{5} - 255056 q^{6} + 65232 q^{7} - 1076876 q^{8} + 2329966 q^{9} + O(q^{10}) \) \( 56 q - 2 q^{2} - 730 q^{3} + 360 q^{4} + 16898 q^{5} - 255056 q^{6} + 65232 q^{7} - 1076876 q^{8} + 2329966 q^{9} + 1809804 q^{10} - 12400678 q^{11} - 36466556 q^{12} + 8510578 q^{13} - 32192740 q^{14} + 58267764 q^{15} + 49054360 q^{16} - 2730008 q^{17} - 134185218 q^{18} + 687321870 q^{19} - 337515748 q^{20} - 336081308 q^{21} + 747130500 q^{22} + 210016880 q^{23} + 4015997104 q^{24} + 262952922 q^{25} - 7112421624 q^{26} - 4083419128 q^{27} + 10814980184 q^{28} - 2896564486 q^{29} - 7391197164 q^{30} - 11253200848 q^{31} + 161064008 q^{32} + 7736141596 q^{33} + 21518457652 q^{34} + 9879664412 q^{35} - 45856853012 q^{36} + 3678703338 q^{37} + 42250712128 q^{38} + 21412862896 q^{39} + 62168140552 q^{40} - 24031840452 q^{41} - 221492896520 q^{42} - 55432077854 q^{43} + 260848874692 q^{44} + 43054154358 q^{45} - 86330105076 q^{46} + 264471315568 q^{47} - 204935679512 q^{48} - 463336677588 q^{49} + 726765984390 q^{50} - 726061876588 q^{51} - 560232726988 q^{52} + 277957136506 q^{53} + 183832923424 q^{54} + 273717035856 q^{55} + 377498473624 q^{56} - 211899133472 q^{57} + 770591295576 q^{58} + 501824598898 q^{59} - 1652643345408 q^{60} - 97879627326 q^{61} + 1409787089968 q^{62} + 1185688664340 q^{63} + 1414847226240 q^{64} - 209787473060 q^{65} - 4165850751116 q^{66} - 1523656277410 q^{67} + 1936048158032 q^{68} + 465968180628 q^{69} - 1514955295360 q^{70} + 3548344800592 q^{71} - 931909002396 q^{72} + 1333995927036 q^{73} + 2967549191692 q^{74} - 8210473363842 q^{75} - 6006275999532 q^{76} - 3754874767516 q^{77} + 33537158300 q^{78} + 16841575183008 q^{79} + 3800056341544 q^{80} - 9667864508880 q^{81} - 1354092283296 q^{82} - 11172077966522 q^{83} + 6692487540136 q^{84} + 3003459133036 q^{85} - 2175364294396 q^{86} + 25789862820912 q^{87} - 2008707597832 q^{88} - 3034933603620 q^{89} + 1744037438232 q^{90} - 26049096512156 q^{91} + 5983522987064 q^{92} + 2836230337616 q^{93} - 10384516980592 q^{94} + 46358111232292 q^{95} - 22107121515856 q^{96} + 6262475466824 q^{97} + 27036562854554 q^{98} - 35014268425898 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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
16.14.a \(\chi_{16}(1, \cdot)\) 16.14.a.a 1 1
16.14.a.b 1
16.14.a.c 1
16.14.a.d 1
16.14.a.e 2
16.14.b \(\chi_{16}(9, \cdot)\) None 0 1
16.14.e \(\chi_{16}(5, \cdot)\) 16.14.e.a 50 2

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

\( S_{14}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)