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Properties

Label 16.15
Level 16
Weight 15
Dimension 61
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(16))\).

Total New Old
Modular forms 119 65 54
Cusp forms 105 61 44
Eisenstein series 14 4 10

Trace form

\( 61 q - 2 q^{2} - 2 q^{3} + 15832 q^{4} - 24188 q^{5} - 182528 q^{6} - 4 q^{7} + 2748484 q^{8} - 21296049 q^{9} + O(q^{10}) \) \( 61 q - 2 q^{2} - 2 q^{3} + 15832 q^{4} - 24188 q^{5} - 182528 q^{6} - 4 q^{7} + 2748484 q^{8} - 21296049 q^{9} + 16861596 q^{10} - 10455538 q^{11} - 87110828 q^{12} + 139092884 q^{13} + 66965260 q^{14} - 1059602728 q^{16} + 710175338 q^{17} + 438192046 q^{18} + 702532062 q^{19} + 1755464396 q^{20} - 1425518324 q^{21} - 4795498204 q^{22} + 9748846012 q^{23} + 6975250608 q^{24} + 11435621981 q^{25} - 8671243576 q^{26} - 17865634112 q^{27} - 1297033864 q^{28} + 50325817796 q^{29} + 11736190852 q^{30} - 33545826552 q^{32} - 2039491588 q^{33} - 50990884972 q^{34} + 125535560540 q^{35} + 60739632140 q^{36} - 148037258220 q^{37} - 763264561040 q^{38} + 207890167484 q^{39} + 1298710786600 q^{40} + 189781331742 q^{41} - 1441334806824 q^{42} + 834144712302 q^{43} - 1390640237388 q^{44} + 332965932312 q^{45} + 2618424802780 q^{46} - 4460553354264 q^{48} + 2207623784985 q^{49} - 14467226554 q^{50} - 109367594148 q^{51} + 700335676036 q^{52} - 5378335711084 q^{53} - 6106962841312 q^{54} + 7743608133372 q^{55} + 892124789080 q^{56} + 8528108338176 q^{57} - 3111214006280 q^{58} - 2886464056530 q^{59} - 5948471456800 q^{60} + 5585418834260 q^{61} + 4387920975408 q^{62} - 11796533376704 q^{64} + 16876690937032 q^{65} + 3599619796132 q^{66} + 16035979669214 q^{67} - 11417990783952 q^{68} + 7106518935916 q^{69} + 6360571783424 q^{70} - 23491285382916 q^{71} - 17358886385420 q^{72} + 10508042495518 q^{73} + 17391872660764 q^{74} + 38233839801842 q^{75} + 8965870021732 q^{76} - 99584530774836 q^{77} - 102277039258452 q^{78} + 184151019521512 q^{80} + 70359254622653 q^{81} - 60118295271632 q^{82} - 44676337597762 q^{83} - 30278459356760 q^{84} - 235117238873192 q^{85} + 200817997017700 q^{86} - 19584321079236 q^{87} - 98329880319368 q^{88} + 110507925483582 q^{89} + 105728657951480 q^{90} + 12075497546300 q^{91} + 263822607742360 q^{92} - 509700272402912 q^{93} + 36585390208368 q^{94} - 124834847268944 q^{96} + 373205288690442 q^{97} + 73723998799370 q^{98} - 130415167656994 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(16))\)

We only show spaces with odd 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
16.15.c \(\chi_{16}(15, \cdot)\) 16.15.c.a 1 1
16.15.c.b 2
16.15.c.c 4
16.15.d \(\chi_{16}(7, \cdot)\) None 0 1
16.15.f \(\chi_{16}(3, \cdot)\) 16.15.f.a 54 2

Decomposition of \(S_{15}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{15}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{15}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)