Properties

Label 396.2
Level 396
Weight 2
Dimension 1879
Nonzero newspaces 16
Newform subspaces 39
Sturm bound 17280
Trace bound 4

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Defining parameters

Level: \( N \) = \( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 39 \)
Sturm bound: \(17280\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(396))\).

Total New Old
Modular forms 4720 2043 2677
Cusp forms 3921 1879 2042
Eisenstein series 799 164 635

Trace form

\( 1879 q - 9 q^{2} - 5 q^{4} - 12 q^{5} - 14 q^{6} + q^{7} - 15 q^{8} - 16 q^{9} + O(q^{10}) \) \( 1879 q - 9 q^{2} - 5 q^{4} - 12 q^{5} - 14 q^{6} + q^{7} - 15 q^{8} - 16 q^{9} - 32 q^{10} - 2 q^{11} - 52 q^{12} - 21 q^{13} - 34 q^{14} - 18 q^{15} - 9 q^{16} - 49 q^{17} - 56 q^{18} + 15 q^{19} - 26 q^{20} - 34 q^{21} + 12 q^{22} + 19 q^{23} - 26 q^{24} + 38 q^{25} + 10 q^{26} + 30 q^{27} + 4 q^{28} + 19 q^{29} + 16 q^{30} + 58 q^{31} + 36 q^{32} - 5 q^{33} - 24 q^{34} + 97 q^{35} + 46 q^{36} + 14 q^{38} + 36 q^{39} - 54 q^{40} + 3 q^{41} - 4 q^{42} + 12 q^{43} - 50 q^{44} - 100 q^{45} - 94 q^{46} - 23 q^{47} - 62 q^{48} - 63 q^{49} - 167 q^{50} - 10 q^{51} - 164 q^{52} - 41 q^{53} - 178 q^{54} - 88 q^{55} - 236 q^{56} - 132 q^{57} - 204 q^{58} - 126 q^{59} - 172 q^{60} - 125 q^{61} - 240 q^{62} - 74 q^{63} - 245 q^{64} - 156 q^{65} - 126 q^{66} - 127 q^{67} - 180 q^{68} - 42 q^{69} - 218 q^{70} - 92 q^{71} - 128 q^{72} - 59 q^{73} - 190 q^{74} - 46 q^{75} - 164 q^{76} - 148 q^{77} - 116 q^{78} - 45 q^{79} - 190 q^{80} - 96 q^{81} - 183 q^{82} - 93 q^{83} - 150 q^{84} - 75 q^{85} - 67 q^{86} - 82 q^{87} - 74 q^{88} - 179 q^{89} - 32 q^{90} + 97 q^{91} - 138 q^{92} - 230 q^{93} - 4 q^{94} - 129 q^{95} - 14 q^{96} - 46 q^{97} - 169 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)

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
396.2.a \(\chi_{396}(1, \cdot)\) 396.2.a.a 1 1
396.2.a.b 1
396.2.a.c 1
396.2.b \(\chi_{396}(197, \cdot)\) 396.2.b.a 2 1
396.2.b.b 2
396.2.c \(\chi_{396}(287, \cdot)\) 396.2.c.a 10 1
396.2.c.b 10
396.2.h \(\chi_{396}(307, \cdot)\) 396.2.h.a 4 1
396.2.h.b 4
396.2.h.c 8
396.2.h.d 12
396.2.i \(\chi_{396}(133, \cdot)\) 396.2.i.a 2 2
396.2.i.b 2
396.2.i.c 2
396.2.i.d 6
396.2.i.e 8
396.2.j \(\chi_{396}(37, \cdot)\) 396.2.j.a 4 4
396.2.j.b 4
396.2.j.c 4
396.2.j.d 8
396.2.k \(\chi_{396}(43, \cdot)\) 396.2.k.a 4 2
396.2.k.b 4
396.2.k.c 4
396.2.k.d 4
396.2.k.e 120
396.2.p \(\chi_{396}(23, \cdot)\) 396.2.p.a 60 2
396.2.p.b 60
396.2.q \(\chi_{396}(65, \cdot)\) 396.2.q.a 4 2
396.2.q.b 4
396.2.q.c 16
396.2.r \(\chi_{396}(19, \cdot)\) 396.2.r.a 16 4
396.2.r.b 48
396.2.r.c 48
396.2.w \(\chi_{396}(71, \cdot)\) 396.2.w.a 96 4
396.2.x \(\chi_{396}(17, \cdot)\) 396.2.x.a 16 4
396.2.y \(\chi_{396}(25, \cdot)\) 396.2.y.a 96 8
396.2.z \(\chi_{396}(29, \cdot)\) 396.2.z.a 96 8
396.2.ba \(\chi_{396}(47, \cdot)\) 396.2.ba.a 544 8
396.2.bf \(\chi_{396}(7, \cdot)\) 396.2.bf.a 544 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(396))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(396)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)