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Properties

Label 9.7
Level 9
Weight 7
Dimension 12
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 42
Trace bound 1

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(42\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(9))\).

Total New Old
Modular forms 22 16 6
Cusp forms 14 12 2
Eisenstein series 8 4 4

Trace form

\( 12 q - 3 q^{2} + 24 q^{3} - 69 q^{4} - 219 q^{5} + 333 q^{6} + 927 q^{7} - 1980 q^{9} + O(q^{10}) \) \( 12 q - 3 q^{2} + 24 q^{3} - 69 q^{4} - 219 q^{5} + 333 q^{6} + 927 q^{7} - 1980 q^{9} - 1752 q^{10} + 483 q^{11} - 1830 q^{12} - 153 q^{13} + 12174 q^{14} + 7965 q^{15} - 3513 q^{16} - 7884 q^{18} + 1536 q^{19} - 63186 q^{20} - 25845 q^{21} + 25503 q^{22} + 53565 q^{23} + 111519 q^{24} + 31602 q^{25} - 101034 q^{27} - 125364 q^{28} - 80679 q^{29} - 37782 q^{30} - 45729 q^{31} + 218295 q^{32} + 229995 q^{33} + 189189 q^{34} - 274977 q^{36} - 35400 q^{37} - 371877 q^{38} - 112749 q^{39} + 109230 q^{40} + 232251 q^{41} + 270540 q^{42} - 275175 q^{43} + 63801 q^{45} - 33936 q^{46} - 142887 q^{47} - 143283 q^{48} + 400092 q^{49} + 318459 q^{50} + 57078 q^{51} + 119496 q^{52} + 13851 q^{54} - 309822 q^{55} + 342546 q^{56} - 1086 q^{57} - 970014 q^{58} - 995061 q^{59} - 1011402 q^{60} + 442971 q^{61} + 526455 q^{63} + 1257834 q^{64} + 1642029 q^{65} + 1610586 q^{66} - 273663 q^{67} - 1693791 q^{68} - 851715 q^{69} - 1153668 q^{70} + 1469907 q^{72} + 317544 q^{73} + 595182 q^{74} - 757524 q^{75} + 1121361 q^{76} - 2198883 q^{77} - 3481884 q^{78} - 611541 q^{79} + 1774548 q^{81} + 732054 q^{82} + 3008337 q^{83} + 1543746 q^{84} - 281124 q^{85} + 1905549 q^{86} - 615591 q^{87} - 1098861 q^{88} + 84294 q^{90} + 148734 q^{91} - 973788 q^{92} - 2954553 q^{93} - 2473644 q^{94} - 2562954 q^{95} - 1022112 q^{96} + 261693 q^{97} - 432567 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)

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
9.7.b \(\chi_{9}(8, \cdot)\) 9.7.b.a 2 1
9.7.d \(\chi_{9}(2, \cdot)\) 9.7.d.a 10 2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 1}\)