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Properties

Label 28.7
Level 28
Weight 7
Dimension 74
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 336
Trace bound 1

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Defining parameters

Level: \( N \) = \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(336\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(28))\).

Total New Old
Modular forms 159 82 77
Cusp forms 129 74 55
Eisenstein series 30 8 22

Trace form

\( 74 q - 11 q^{2} + 221 q^{4} + 122 q^{5} - 966 q^{6} - 480 q^{7} + 1147 q^{8} + 2766 q^{9} + O(q^{10}) \) \( 74 q - 11 q^{2} + 221 q^{4} + 122 q^{5} - 966 q^{6} - 480 q^{7} + 1147 q^{8} + 2766 q^{9} - 650 q^{10} - 756 q^{11} - 9618 q^{12} - 5876 q^{13} + 11193 q^{14} + 4824 q^{15} + 1121 q^{16} + 28970 q^{17} - 11193 q^{18} - 10836 q^{19} - 37960 q^{20} + 5718 q^{21} - 15096 q^{22} - 31584 q^{23} + 99294 q^{24} + 17490 q^{25} + 16952 q^{26} - 34587 q^{28} + 21884 q^{29} - 178758 q^{30} + 13524 q^{31} - 62981 q^{32} + 249822 q^{33} + 238462 q^{34} - 81444 q^{35} - 24675 q^{36} - 240914 q^{37} - 98292 q^{38} - 266196 q^{39} - 172028 q^{40} - 117460 q^{41} + 270690 q^{42} + 346536 q^{43} + 195348 q^{44} + 538860 q^{45} - 237858 q^{46} + 30156 q^{47} + 390174 q^{48} - 292990 q^{49} - 125211 q^{50} - 906948 q^{51} + 349924 q^{52} + 258590 q^{53} - 102498 q^{54} - 87969 q^{56} - 254820 q^{57} + 167962 q^{58} + 985992 q^{59} - 601848 q^{60} + 552286 q^{61} + 624696 q^{62} - 1437600 q^{63} - 758359 q^{64} - 1650872 q^{65} + 614298 q^{66} - 1499568 q^{67} - 85270 q^{68} + 1767300 q^{69} - 987966 q^{70} + 1722840 q^{71} - 1040913 q^{72} + 2573326 q^{73} + 1203704 q^{74} + 2230704 q^{75} + 3368946 q^{76} - 2714310 q^{77} + 490152 q^{78} - 3286752 q^{79} - 298408 q^{80} - 3087864 q^{81} - 1457606 q^{82} + 1606290 q^{84} + 4740236 q^{85} - 1381620 q^{86} + 6079500 q^{87} - 875808 q^{88} + 2725286 q^{89} - 6932268 q^{90} - 1021896 q^{91} - 4589256 q^{92} - 8894154 q^{93} + 25254 q^{94} - 4347168 q^{95} - 1533366 q^{96} - 3651908 q^{97} + 2551297 q^{98} + 5133312 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(28))\)

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
28.7.b \(\chi_{28}(13, \cdot)\) 28.7.b.a 4 1
28.7.c \(\chi_{28}(15, \cdot)\) 28.7.c.a 18 1
28.7.g \(\chi_{28}(11, \cdot)\) 28.7.g.a 44 2
28.7.h \(\chi_{28}(5, \cdot)\) 28.7.h.a 8 2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(28))\) into lower level spaces

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