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Properties

Label 374.2
Level 374
Weight 2
Dimension 1409
Nonzero newspaces 10
Newform subspaces 29
Sturm bound 17280
Trace bound 3

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Defining parameters

Level: \( N \) = \( 374 = 2 \cdot 11 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 29 \)
Sturm bound: \(17280\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(374))\).

Total New Old
Modular forms 4640 1409 3231
Cusp forms 4001 1409 2592
Eisenstein series 639 0 639

Trace form

\( 1409 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 2 q^{6} + 4 q^{7} + 3 q^{8} - q^{9} + O(q^{10}) \) \( 1409 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 2 q^{6} + 4 q^{7} + 3 q^{8} - q^{9} - 10 q^{10} - 13 q^{11} - 24 q^{12} - 10 q^{13} - 28 q^{14} - 84 q^{15} - 5 q^{16} - 17 q^{17} - 35 q^{18} - 2 q^{19} + 10 q^{20} - 40 q^{21} + 7 q^{22} - 14 q^{24} - 59 q^{25} - 6 q^{26} - 18 q^{27} + 4 q^{28} - 30 q^{29} + 12 q^{30} - 28 q^{31} - 7 q^{32} - 50 q^{33} + 15 q^{34} - 40 q^{35} + 29 q^{36} + 10 q^{37} - 16 q^{38} - 60 q^{39} - 2 q^{40} - 90 q^{41} - 60 q^{42} - 80 q^{43} - 39 q^{44} - 34 q^{45} - 32 q^{46} - 96 q^{47} + 12 q^{48} - 77 q^{49} - 59 q^{50} - 53 q^{51} - 62 q^{52} - 74 q^{53} - 72 q^{54} - 82 q^{55} + 24 q^{56} - 106 q^{57} - 54 q^{58} - 110 q^{59} - 32 q^{60} - 50 q^{61} - 60 q^{62} - 120 q^{63} + 3 q^{64} - 20 q^{65} - 36 q^{66} - 8 q^{67} + 7 q^{68} - 60 q^{69} - 40 q^{71} - 41 q^{72} - 66 q^{73} + 2 q^{74} - 82 q^{75} + 40 q^{76} - 56 q^{77} - 40 q^{78} - 20 q^{79} - 34 q^{80} - 115 q^{81} - 80 q^{82} - 22 q^{83} - 48 q^{84} - 164 q^{85} - 62 q^{86} - 128 q^{87} - 29 q^{88} - 82 q^{89} - 82 q^{90} - 184 q^{91} - 20 q^{92} - 132 q^{93} - 104 q^{94} - 148 q^{95} + 12 q^{96} - 88 q^{97} + 9 q^{98} - 145 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(374))\)

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
374.2.a \(\chi_{374}(1, \cdot)\) 374.2.a.a 1 1
374.2.a.b 3
374.2.a.c 3
374.2.a.d 4
374.2.a.e 4
374.2.b \(\chi_{374}(67, \cdot)\) 374.2.b.a 6 1
374.2.b.b 8
374.2.f \(\chi_{374}(89, \cdot)\) 374.2.f.a 12 2
374.2.f.b 16
374.2.g \(\chi_{374}(69, \cdot)\) 374.2.g.a 4 4
374.2.g.b 4
374.2.g.c 4
374.2.g.d 8
374.2.g.e 8
374.2.g.f 16
374.2.g.g 20
374.2.h \(\chi_{374}(111, \cdot)\) 374.2.h.a 8 4
374.2.h.b 24
374.2.h.c 32
374.2.l \(\chi_{374}(135, \cdot)\) 374.2.l.a 32 4
374.2.l.b 40
374.2.m \(\chi_{374}(65, \cdot)\) 374.2.m.a 72 8
374.2.m.b 72
374.2.o \(\chi_{374}(47, \cdot)\) 374.2.o.a 64 8
374.2.o.b 80
374.2.r \(\chi_{374}(9, \cdot)\) 374.2.r.a 128 16
374.2.r.b 160
374.2.t \(\chi_{374}(7, \cdot)\) 374.2.t.a 288 32
374.2.t.b 288

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(374))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(374)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 2}\)