Properties

Label 354.2
Level 354
Weight 2
Dimension 871
Nonzero newspaces 4
Newforms 16
Sturm bound 13920
Trace bound 1

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newforms: \( 16 \)
Sturm bound: \(13920\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(354))\).

Total New Old
Modular forms 3712 871 2841
Cusp forms 3249 871 2378
Eisenstein series 463 0 463

Trace form

\(871q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(871q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut q^{12} \) \(\mathstrut +\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut +\mathstrut 6q^{20} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut +\mathstrut 14q^{26} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 30q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut +\mathstrut 32q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 18q^{34} \) \(\mathstrut +\mathstrut 48q^{35} \) \(\mathstrut +\mathstrut q^{36} \) \(\mathstrut +\mathstrut 38q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 42q^{41} \) \(\mathstrut +\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 44q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut -\mathstrut 52q^{45} \) \(\mathstrut -\mathstrut 92q^{46} \) \(\mathstrut -\mathstrut 68q^{47} \) \(\mathstrut +\mathstrut q^{48} \) \(\mathstrut -\mathstrut 175q^{49} \) \(\mathstrut -\mathstrut 201q^{50} \) \(\mathstrut -\mathstrut 214q^{51} \) \(\mathstrut -\mathstrut 102q^{52} \) \(\mathstrut -\mathstrut 178q^{53} \) \(\mathstrut -\mathstrut 202q^{54} \) \(\mathstrut -\mathstrut 276q^{55} \) \(\mathstrut +\mathstrut 8q^{56} \) \(\mathstrut -\mathstrut 270q^{57} \) \(\mathstrut -\mathstrut 86q^{58} \) \(\mathstrut -\mathstrut 173q^{59} \) \(\mathstrut -\mathstrut 168q^{60} \) \(\mathstrut -\mathstrut 170q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 282q^{63} \) \(\mathstrut +\mathstrut q^{64} \) \(\mathstrut -\mathstrut 264q^{65} \) \(\mathstrut -\mathstrut 191q^{66} \) \(\mathstrut -\mathstrut 164q^{67} \) \(\mathstrut -\mathstrut 98q^{68} \) \(\mathstrut -\mathstrut 208q^{69} \) \(\mathstrut -\mathstrut 184q^{70} \) \(\mathstrut -\mathstrut 160q^{71} \) \(\mathstrut +\mathstrut q^{72} \) \(\mathstrut -\mathstrut 42q^{73} \) \(\mathstrut -\mathstrut 78q^{74} \) \(\mathstrut -\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 80q^{79} \) \(\mathstrut +\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut +\mathstrut 42q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 108q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 90q^{89} \) \(\mathstrut +\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 112q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut +\mathstrut 120q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 57q^{98} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(354))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
354.2.a \(\chi_{354}(1, \cdot)\) 354.2.a.a 1 1
354.2.a.b 1
354.2.a.c 1
354.2.a.d 1
354.2.a.e 1
354.2.a.f 1
354.2.a.g 2
354.2.a.h 3
354.2.c \(\chi_{354}(353, \cdot)\) 354.2.c.a 10 1
354.2.c.b 10
354.2.e \(\chi_{354}(7, \cdot)\) 354.2.e.a 56 28
354.2.e.b 56
354.2.e.c 84
354.2.e.d 84
354.2.g \(\chi_{354}(11, \cdot)\) 354.2.g.a 280 28
354.2.g.b 280

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(354))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(354)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)