Properties

Label 28.3
Level 28
Weight 3
Dimension 22
Nonzero newspaces 4
Newforms 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: \( 4 \)
Newforms: \( 4 \)
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

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

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 the 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

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