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Properties

Label 16.7
Level 16
Weight 7
Dimension 25
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 112
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(112\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(16))\).

Total New Old
Modular forms 55 29 26
Cusp forms 41 25 16
Eisenstein series 14 4 10

Trace form

\( 25 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 68 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} + 651 q^{9} + O(q^{10}) \) \( 25 q - 2 q^{2} - 2 q^{3} + 88 q^{4} - 68 q^{5} - 512 q^{6} - 4 q^{7} + 964 q^{8} + 651 q^{9} - 1124 q^{10} + 1358 q^{11} - 2348 q^{12} - 3764 q^{13} + 7564 q^{14} - 7976 q^{16} + 13922 q^{17} - 1874 q^{18} + 3934 q^{19} - 16564 q^{20} - 35252 q^{21} + 25252 q^{22} - 13124 q^{23} - 32592 q^{24} + 52881 q^{25} + 58952 q^{26} + 35776 q^{27} + 45176 q^{28} - 86596 q^{29} + 8452 q^{30} - 39672 q^{32} + 50684 q^{33} - 52588 q^{34} - 112420 q^{35} - 138484 q^{36} - 74612 q^{37} - 187280 q^{38} + 254396 q^{39} + 165160 q^{40} + 49302 q^{41} + 353496 q^{42} - 267986 q^{43} + 380724 q^{44} + 214992 q^{45} + 248156 q^{46} - 460824 q^{48} - 222411 q^{49} - 719674 q^{50} + 301788 q^{51} - 784892 q^{52} - 31348 q^{53} - 547552 q^{54} - 232708 q^{55} + 366424 q^{56} - 118272 q^{57} + 1441912 q^{58} + 39150 q^{59} + 2405600 q^{60} + 1174924 q^{61} + 182832 q^{62} - 318656 q^{64} - 812168 q^{65} - 3392732 q^{66} - 122786 q^{67} - 2504400 q^{68} - 1013204 q^{69} - 1186816 q^{70} - 267012 q^{71} + 1748596 q^{72} + 758934 q^{73} + 3610396 q^{74} - 275278 q^{75} + 4245988 q^{76} + 1346316 q^{77} + 3179052 q^{78} - 2898968 q^{80} - 939559 q^{81} - 5004624 q^{82} - 288322 q^{83} - 7602776 q^{84} - 2128312 q^{85} - 3240476 q^{86} + 2029884 q^{87} + 3308152 q^{88} + 2322870 q^{89} + 10273400 q^{90} + 302396 q^{91} + 7253656 q^{92} - 1062752 q^{93} + 3859056 q^{94} - 5689424 q^{96} + 348674 q^{97} - 9176950 q^{98} - 271522 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.7.c \(\chi_{16}(15, \cdot)\) 16.7.c.a 1 1
16.7.c.b 2
16.7.d \(\chi_{16}(7, \cdot)\) None 0 1
16.7.f \(\chi_{16}(3, \cdot)\) 16.7.f.a 22 2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)