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Properties

Label 738.2
Level 738
Weight 2
Dimension 3986
Nonzero newspaces 16
Newform subspaces 90
Sturm bound 60480
Trace bound 2

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Defining parameters

Level: \( N \) = \( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 90 \)
Sturm bound: \(60480\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(738))\).

Total New Old
Modular forms 15760 3986 11774
Cusp forms 14481 3986 10495
Eisenstein series 1279 0 1279

Trace form

\( 3986 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} + O(q^{10}) \) \( 3986 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} - 6 q^{11} + 4 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + 12 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{24} - 10 q^{25} - 8 q^{26} - 8 q^{28} + 12 q^{29} + 32 q^{31} + 12 q^{32} + 18 q^{33} + 44 q^{34} + 80 q^{35} - 6 q^{36} + 136 q^{37} + 38 q^{38} + 40 q^{40} + 49 q^{41} + 38 q^{43} + 52 q^{44} + 64 q^{46} + 108 q^{47} - 6 q^{48} + 74 q^{49} + 40 q^{50} - 18 q^{51} + 14 q^{52} - 8 q^{53} - 18 q^{54} + 4 q^{56} - 6 q^{57} + 12 q^{58} + 6 q^{59} + 16 q^{61} + 16 q^{62} + 24 q^{63} - 4 q^{64} + 10 q^{65} + 70 q^{67} - 6 q^{68} + 128 q^{71} - 6 q^{72} + 36 q^{73} - 8 q^{74} + 30 q^{75} - 2 q^{76} + 68 q^{77} + 12 q^{78} + 72 q^{79} + 18 q^{81} - 18 q^{82} + 104 q^{83} + 12 q^{84} + 170 q^{85} - 2 q^{86} - 36 q^{87} - 6 q^{88} + 56 q^{89} + 144 q^{91} - 12 q^{92} - 12 q^{94} + 80 q^{95} + 90 q^{97} + 12 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(738))\)

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
738.2.a \(\chi_{738}(1, \cdot)\) 738.2.a.a 1 1
738.2.a.b 1
738.2.a.c 1
738.2.a.d 1
738.2.a.e 1
738.2.a.f 1
738.2.a.g 1
738.2.a.h 1
738.2.a.i 1
738.2.a.j 1
738.2.a.k 2
738.2.a.l 3
738.2.a.m 3
738.2.d \(\chi_{738}(163, \cdot)\) 738.2.d.a 2 1
738.2.d.b 2
738.2.d.c 2
738.2.d.d 2
738.2.d.e 2
738.2.d.f 2
738.2.d.g 2
738.2.d.h 4
738.2.e \(\chi_{738}(247, \cdot)\) 738.2.e.a 2 2
738.2.e.b 2
738.2.e.c 2
738.2.e.d 2
738.2.e.e 2
738.2.e.f 6
738.2.e.g 8
738.2.e.h 8
738.2.e.i 12
738.2.e.j 14
738.2.e.k 22
738.2.f \(\chi_{738}(73, \cdot)\) 738.2.f.a 2 2
738.2.f.b 2
738.2.f.c 2
738.2.f.d 2
738.2.f.e 2
738.2.f.f 4
738.2.f.g 4
738.2.f.h 8
738.2.f.i 8
738.2.h \(\chi_{738}(37, \cdot)\) 738.2.h.a 4 4
738.2.h.b 4
738.2.h.c 4
738.2.h.d 4
738.2.h.e 4
738.2.h.f 4
738.2.h.g 8
738.2.h.h 8
738.2.h.i 16
738.2.h.j 16
738.2.i \(\chi_{738}(409, \cdot)\) 738.2.i.a 4 2
738.2.i.b 36
738.2.i.c 44
738.2.m \(\chi_{738}(161, \cdot)\) 738.2.m.a 4 4
738.2.m.b 4
738.2.m.c 8
738.2.m.d 8
738.2.m.e 16
738.2.m.f 16
738.2.n \(\chi_{738}(127, \cdot)\) 738.2.n.a 4 4
738.2.n.b 4
738.2.n.c 8
738.2.n.d 8
738.2.n.e 8
738.2.n.f 12
738.2.n.g 12
738.2.n.h 16
738.2.r \(\chi_{738}(319, \cdot)\) 738.2.r.a 80 4
738.2.r.b 88
738.2.s \(\chi_{738}(133, \cdot)\) 738.2.s.a 160 8
738.2.s.b 176
738.2.u \(\chi_{738}(289, \cdot)\) 738.2.u.a 8 8
738.2.u.b 16
738.2.u.c 24
738.2.u.d 24
738.2.u.e 32
738.2.u.f 32
738.2.v \(\chi_{738}(137, \cdot)\) 738.2.v.a 168 8
738.2.v.b 168
738.2.z \(\chi_{738}(25, \cdot)\) 738.2.z.a 160 8
738.2.z.b 176
738.2.ba \(\chi_{738}(17, \cdot)\) 738.2.ba.a 48 16
738.2.ba.b 48
738.2.ba.c 64
738.2.ba.d 64
738.2.bc \(\chi_{738}(43, \cdot)\) 738.2.bc.a 320 16
738.2.bc.b 352
738.2.bf \(\chi_{738}(11, \cdot)\) 738.2.bf.a 672 32
738.2.bf.b 672

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(738))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(738)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(369))\)\(^{\oplus 2}\)