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Properties

Label 372.2
Level 372
Weight 2
Dimension 1620
Nonzero newspaces 16
Newform subspaces 36
Sturm bound 15360
Trace bound 3

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Defining parameters

Level: \( N \) = \( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 36 \)
Sturm bound: \(15360\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(372))\).

Total New Old
Modular forms 4140 1732 2408
Cusp forms 3541 1620 1921
Eisenstein series 599 112 487

Trace form

\( 1620 q - 30 q^{4} - 15 q^{6} - 30 q^{9} + O(q^{10}) \) \( 1620 q - 30 q^{4} - 15 q^{6} - 30 q^{9} - 30 q^{10} - 15 q^{12} - 60 q^{13} - 30 q^{16} - 15 q^{18} - 25 q^{21} - 30 q^{22} + 30 q^{23} - 15 q^{24} + 10 q^{25} - 30 q^{28} + 60 q^{29} - 30 q^{30} + 60 q^{31} - 30 q^{34} + 60 q^{35} - 15 q^{36} + 30 q^{37} + 35 q^{39} - 30 q^{40} + 30 q^{41} - 15 q^{42} + 10 q^{43} - 30 q^{45} - 30 q^{46} - 60 q^{48} - 120 q^{49} - 150 q^{50} - 90 q^{51} - 180 q^{52} - 60 q^{53} - 180 q^{54} - 120 q^{55} - 270 q^{56} - 120 q^{57} - 240 q^{58} - 60 q^{59} - 240 q^{60} - 300 q^{61} - 180 q^{62} - 120 q^{63} - 210 q^{64} - 180 q^{65} - 240 q^{66} - 60 q^{67} - 210 q^{68} - 120 q^{69} - 300 q^{70} - 120 q^{71} - 180 q^{72} - 120 q^{73} - 150 q^{74} - 105 q^{75} - 180 q^{76} - 60 q^{77} - 60 q^{78} - 90 q^{81} - 30 q^{82} - 15 q^{84} - 60 q^{85} - 60 q^{87} - 30 q^{88} - 15 q^{90} - 150 q^{93} - 60 q^{94} - 60 q^{96} - 60 q^{97} - 75 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(372))\)

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
372.2.a \(\chi_{372}(1, \cdot)\) 372.2.a.a 1 1
372.2.a.b 1
372.2.a.c 1
372.2.a.d 1
372.2.a.e 2
372.2.c \(\chi_{372}(311, \cdot)\) 372.2.c.a 4 1
372.2.c.b 4
372.2.c.c 4
372.2.c.d 48
372.2.e \(\chi_{372}(185, \cdot)\) 372.2.e.a 2 1
372.2.e.b 8
372.2.g \(\chi_{372}(247, \cdot)\) 372.2.g.a 16 1
372.2.g.b 16
372.2.i \(\chi_{372}(25, \cdot)\) 372.2.i.a 4 2
372.2.i.b 6
372.2.j \(\chi_{372}(97, \cdot)\) 372.2.j.a 4 4
372.2.j.b 8
372.2.j.c 12
372.2.l \(\chi_{372}(223, \cdot)\) 372.2.l.a 32 2
372.2.l.b 32
372.2.n \(\chi_{372}(161, \cdot)\) 372.2.n.a 2 2
372.2.n.b 20
372.2.p \(\chi_{372}(191, \cdot)\) 372.2.p.a 120 2
372.2.r \(\chi_{372}(29, \cdot)\) 372.2.r.a 8 4
372.2.r.b 8
372.2.r.c 24
372.2.t \(\chi_{372}(35, \cdot)\) 372.2.t.a 240 4
372.2.w \(\chi_{372}(91, \cdot)\) 372.2.w.a 64 4
372.2.w.b 64
372.2.y \(\chi_{372}(49, \cdot)\) 372.2.y.a 16 8
372.2.y.b 24
372.2.ba \(\chi_{372}(43, \cdot)\) 372.2.ba.a 128 8
372.2.ba.b 128
372.2.bd \(\chi_{372}(59, \cdot)\) 372.2.bd.a 480 8
372.2.bf \(\chi_{372}(17, \cdot)\) 372.2.bf.a 8 8
372.2.bf.b 80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(372))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(372)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 2}\)