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Properties

Label 28.3
Level 28
Weight 3
Dimension 22
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 144
Trace bound 3

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Defining parameters

Level: \( N \) = \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(28))\).

Total New Old
Modular forms 63 30 33
Cusp forms 33 22 11
Eisenstein series 30 8 22

Trace form

\( 22 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} - 42 q^{9} + O(q^{10}) \) \( 22 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} - 6 q^{6} - 4 q^{7} - 21 q^{8} - 42 q^{9} - 30 q^{10} - 27 q^{11} - 18 q^{12} - 12 q^{13} + 9 q^{14} + 54 q^{15} + 33 q^{16} + 45 q^{17} + 99 q^{18} + 27 q^{19} + 120 q^{20} - 51 q^{21} + 96 q^{22} - 51 q^{23} + 78 q^{24} - 50 q^{25} - 27 q^{28} + 12 q^{29} - 138 q^{30} - 21 q^{31} - 213 q^{32} + 21 q^{33} - 258 q^{34} - 69 q^{35} - 291 q^{36} + 103 q^{37} - 192 q^{38} - 24 q^{39} - 108 q^{40} - 12 q^{41} + 138 q^{42} + 40 q^{43} + 228 q^{44} + 150 q^{45} + 282 q^{46} + 75 q^{47} + 414 q^{48} + 166 q^{49} + 369 q^{50} + 243 q^{51} + 228 q^{52} + 255 q^{53} + 138 q^{54} - 33 q^{56} - 246 q^{57} - 342 q^{58} - 141 q^{59} - 408 q^{60} - 219 q^{61} - 384 q^{62} - 108 q^{63} - 375 q^{64} - 252 q^{65} - 306 q^{66} - 91 q^{67} - 6 q^{68} - 348 q^{69} + 174 q^{70} - 168 q^{71} + 303 q^{72} - 411 q^{73} + 540 q^{74} - 66 q^{75} + 498 q^{76} - 105 q^{77} + 312 q^{78} + 221 q^{79} + 312 q^{80} - 63 q^{81} + 186 q^{82} - 126 q^{84} - 54 q^{85} - 180 q^{86} - 18 q^{87} - 288 q^{88} + 453 q^{89} - 588 q^{90} + 48 q^{91} - 552 q^{92} + 429 q^{93} - 174 q^{94} + 267 q^{95} - 150 q^{96} + 996 q^{97} - 183 q^{98} + 360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)

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
28.3.b \(\chi_{28}(13, \cdot)\) 28.3.b.a 2 1
28.3.c \(\chi_{28}(15, \cdot)\) 28.3.c.a 6 1
28.3.g \(\chi_{28}(11, \cdot)\) 28.3.g.a 12 2
28.3.h \(\chi_{28}(5, \cdot)\) 28.3.h.a 2 2

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(28))\) into lower level spaces

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