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Properties

Label 28.6
Level 28
Weight 6
Dimension 62
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 288
Trace bound 1

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Defining parameters

Level: \( N \) = \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(288\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(28))\).

Total New Old
Modular forms 135 74 61
Cusp forms 105 62 43
Eisenstein series 30 12 18

Trace form

\( 62 q - 3 q^{2} + 15 q^{3} - 3 q^{4} - 147 q^{5} - 28 q^{7} + 261 q^{8} - 54 q^{9} + O(q^{10}) \) \( 62 q - 3 q^{2} + 15 q^{3} - 3 q^{4} - 147 q^{5} - 28 q^{7} + 261 q^{8} - 54 q^{9} - 804 q^{10} - 813 q^{11} + 1632 q^{12} + 532 q^{13} + 1857 q^{14} + 3678 q^{15} - 1143 q^{16} - 2019 q^{17} - 6747 q^{18} - 4559 q^{19} - 8877 q^{21} + 13206 q^{22} + 6393 q^{23} + 564 q^{24} + 7592 q^{25} - 8892 q^{26} + 12726 q^{27} - 16827 q^{28} + 15516 q^{29} + 5364 q^{30} - 6293 q^{31} + 8397 q^{32} - 36945 q^{33} - 36393 q^{35} - 10011 q^{36} - 11831 q^{37} - 5652 q^{38} + 41478 q^{39} + 35052 q^{40} + 29232 q^{41} + 30756 q^{42} + 63136 q^{43} + 20094 q^{44} + 7554 q^{45} + 16242 q^{46} - 58923 q^{47} - 51034 q^{49} - 79551 q^{50} - 38547 q^{51} - 61776 q^{52} + 11541 q^{53} - 30996 q^{54} + 130662 q^{55} + 27729 q^{56} + 42798 q^{57} - 112734 q^{58} - 45057 q^{59} - 118680 q^{60} - 86219 q^{61} - 178626 q^{63} + 99945 q^{64} + 109026 q^{65} + 221808 q^{66} + 112567 q^{67} + 25020 q^{68} + 136458 q^{69} + 160488 q^{70} + 149184 q^{71} + 259401 q^{72} - 293459 q^{73} + 267870 q^{74} - 228948 q^{75} - 128985 q^{77} - 216552 q^{78} - 16559 q^{79} - 277224 q^{80} + 457635 q^{81} - 391836 q^{82} - 43008 q^{83} - 573972 q^{84} + 95226 q^{85} - 274818 q^{86} - 81234 q^{87} - 198990 q^{88} - 163515 q^{89} - 81032 q^{91} + 288954 q^{92} - 268161 q^{93} + 359988 q^{94} - 63393 q^{95} + 1061736 q^{96} + 409024 q^{97} + 828393 q^{98} + 381828 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(28))\)

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
28.6.a \(\chi_{28}(1, \cdot)\) 28.6.a.a 1 1
28.6.a.b 1
28.6.d \(\chi_{28}(27, \cdot)\) 28.6.d.a 2 1
28.6.d.b 16
28.6.e \(\chi_{28}(9, \cdot)\) 28.6.e.a 2 2
28.6.e.b 4
28.6.f \(\chi_{28}(3, \cdot)\) 28.6.f.a 36 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(28))\) into lower level spaces

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