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Properties

Label 28.8
Level 28
Weight 8
Dimension 92
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 384
Trace bound 1

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Defining parameters

Level: \( N \) = \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(384\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(28))\).

Total New Old
Modular forms 183 104 79
Cusp forms 153 92 61
Eisenstein series 30 12 18

Trace form

\( 92 q - 3 q^{2} + 27 q^{3} - 3 q^{4} - 9 q^{5} + 332 q^{7} - 867 q^{8} - 5184 q^{9} + O(q^{10}) \) \( 92 q - 3 q^{2} + 27 q^{3} - 3 q^{4} - 9 q^{5} + 332 q^{7} - 867 q^{8} - 5184 q^{9} + 9708 q^{10} + 10335 q^{11} - 13848 q^{12} - 31328 q^{13} - 19647 q^{14} + 15918 q^{15} + 47721 q^{16} - 9837 q^{17} + 25581 q^{18} + 11005 q^{19} - 34659 q^{21} - 29490 q^{22} + 9321 q^{23} - 142644 q^{24} - 153802 q^{25} + 205116 q^{26} + 55710 q^{27} + 417285 q^{28} - 102240 q^{29} - 9540 q^{30} - 35861 q^{31} - 1348203 q^{32} + 643869 q^{33} + 906963 q^{35} + 2521149 q^{36} - 765485 q^{37} + 404100 q^{38} - 533346 q^{39} - 1872348 q^{40} - 2262948 q^{41} - 2942340 q^{42} - 1208984 q^{43} + 1624158 q^{44} + 3246186 q^{45} + 3456402 q^{46} + 1869093 q^{47} + 631412 q^{49} - 2861151 q^{50} - 195471 q^{51} - 3374784 q^{52} - 3128601 q^{53} + 5449860 q^{54} - 1136538 q^{55} + 3777489 q^{56} - 4732614 q^{57} - 4692078 q^{58} + 1161459 q^{59} - 3444432 q^{60} + 5289295 q^{61} + 12004710 q^{63} + 2674617 q^{64} + 4600014 q^{65} + 1899192 q^{66} - 5537021 q^{67} - 3418884 q^{68} - 24142770 q^{69} - 399624 q^{70} - 13279392 q^{71} - 8177415 q^{72} + 6871315 q^{73} - 8501106 q^{74} + 38150052 q^{75} + 36769593 q^{77} + 9240072 q^{78} + 2832073 q^{79} + 24461112 q^{80} - 44763117 q^{81} - 12674916 q^{82} - 41841048 q^{83} - 12815124 q^{84} - 39615042 q^{85} + 23964678 q^{86} + 25583382 q^{87} + 22325874 q^{88} + 69189915 q^{89} + 43871512 q^{91} - 39725286 q^{92} + 11401641 q^{93} - 16365540 q^{94} - 50914329 q^{95} + 15981144 q^{96} - 43794260 q^{97} + 16573521 q^{98} - 95711028 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(28))\)

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
28.8.a \(\chi_{28}(1, \cdot)\) 28.8.a.a 2 1
28.8.a.b 2
28.8.d \(\chi_{28}(27, \cdot)\) 28.8.d.a 2 1
28.8.d.b 24
28.8.e \(\chi_{28}(9, \cdot)\) 28.8.e.a 10 2
28.8.f \(\chi_{28}(3, \cdot)\) 28.8.f.a 52 2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(28))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(28)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 1}\)