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Properties

Label 1476.2
Level 1476
Weight 2
Dimension 27544
Nonzero newspaces 32
Sturm bound 241920
Trace bound 16

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Defining parameters

Level: \( N \) = \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(241920\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1476))\).

Total New Old
Modular forms 62080 28248 33832
Cusp forms 58881 27544 31337
Eisenstein series 3199 704 2495

Trace form

\( 27544 q - 54 q^{2} - 50 q^{4} - 102 q^{5} - 74 q^{6} + 6 q^{7} - 60 q^{8} - 136 q^{9} + O(q^{10}) \) \( 27544 q - 54 q^{2} - 50 q^{4} - 102 q^{5} - 74 q^{6} + 6 q^{7} - 60 q^{8} - 136 q^{9} - 172 q^{10} + 6 q^{11} - 92 q^{12} - 106 q^{13} - 84 q^{14} - 18 q^{15} - 74 q^{16} - 144 q^{17} - 116 q^{18} - 96 q^{20} - 154 q^{21} - 66 q^{22} - 6 q^{23} - 86 q^{24} - 102 q^{25} - 60 q^{26} - 156 q^{28} - 126 q^{29} - 44 q^{30} - 2 q^{31} + 6 q^{32} - 190 q^{33} - 34 q^{34} - 28 q^{35} - 14 q^{36} - 400 q^{37} - 6 q^{38} + 6 q^{39} - 44 q^{40} - 161 q^{41} - 124 q^{42} - 38 q^{43} - 60 q^{44} - 190 q^{45} - 204 q^{46} - 78 q^{47} - 122 q^{48} - 198 q^{49} - 102 q^{50} - 124 q^{52} - 116 q^{53} - 158 q^{54} - 36 q^{55} - 96 q^{56} - 172 q^{57} - 124 q^{58} - 6 q^{59} - 92 q^{60} - 130 q^{61} - 60 q^{62} + 6 q^{63} - 200 q^{64} - 56 q^{65} - 32 q^{66} + 78 q^{67} + 70 q^{68} - 82 q^{69} + 152 q^{70} + 128 q^{71} - 38 q^{72} - 164 q^{73} + 120 q^{74} + 24 q^{75} + 246 q^{76} + 14 q^{77} - 56 q^{78} + 110 q^{79} + 140 q^{80} - 136 q^{81} + 46 q^{82} + 62 q^{83} - 140 q^{84} + 30 q^{85} + 98 q^{86} + 18 q^{87} + 182 q^{88} - 64 q^{89} - 92 q^{90} + 172 q^{91} + 12 q^{92} - 250 q^{93} + 156 q^{94} + 56 q^{95} - 104 q^{96} - 86 q^{97} + 40 q^{98} - 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1476))\)

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
1476.2.a \(\chi_{1476}(1, \cdot)\) 1476.2.a.a 1 1
1476.2.a.b 1
1476.2.a.c 2
1476.2.a.d 2
1476.2.a.e 3
1476.2.a.f 3
1476.2.a.g 4
1476.2.c \(\chi_{1476}(575, \cdot)\) 1476.2.c.a 80 1
1476.2.d \(\chi_{1476}(1475, \cdot)\) 1476.2.d.a 4 1
1476.2.d.b 8
1476.2.d.c 8
1476.2.d.d 64
1476.2.f \(\chi_{1476}(901, \cdot)\) 1476.2.f.a 2 1
1476.2.f.b 2
1476.2.f.c 4
1476.2.f.d 4
1476.2.f.e 6
1476.2.i \(\chi_{1476}(493, \cdot)\) 1476.2.i.a 2 2
1476.2.i.b 32
1476.2.i.c 46
1476.2.k \(\chi_{1476}(73, \cdot)\) 1476.2.k.a 6 2
1476.2.k.b 12
1476.2.k.c 16
1476.2.m \(\chi_{1476}(647, \cdot)\) n/a 168 2
1476.2.n \(\chi_{1476}(37, \cdot)\) 1476.2.n.a 4 4
1476.2.n.b 4
1476.2.n.c 4
1476.2.n.d 4
1476.2.n.e 8
1476.2.n.f 16
1476.2.n.g 32
1476.2.q \(\chi_{1476}(409, \cdot)\) 1476.2.q.a 8 2
1476.2.q.b 76
1476.2.s \(\chi_{1476}(491, \cdot)\) n/a 496 2
1476.2.t \(\chi_{1476}(83, \cdot)\) n/a 480 2
1476.2.x \(\chi_{1476}(161, \cdot)\) 1476.2.x.a 28 4
1476.2.x.b 28
1476.2.y \(\chi_{1476}(55, \cdot)\) n/a 412 4
1476.2.bb \(\chi_{1476}(433, \cdot)\) 1476.2.bb.a 8 4
1476.2.bb.b 16
1476.2.bb.c 24
1476.2.bb.d 24
1476.2.bd \(\chi_{1476}(107, \cdot)\) n/a 336 4
1476.2.be \(\chi_{1476}(215, \cdot)\) n/a 336 4
1476.2.bg \(\chi_{1476}(155, \cdot)\) n/a 992 4
1476.2.bi \(\chi_{1476}(337, \cdot)\) n/a 168 4
1476.2.bk \(\chi_{1476}(133, \cdot)\) n/a 336 8
1476.2.bl \(\chi_{1476}(143, \cdot)\) n/a 672 8
1476.2.bn \(\chi_{1476}(289, \cdot)\) n/a 136 8
1476.2.bp \(\chi_{1476}(79, \cdot)\) n/a 1984 8
1476.2.bq \(\chi_{1476}(137, \cdot)\) n/a 336 8
1476.2.bu \(\chi_{1476}(59, \cdot)\) n/a 1984 8
1476.2.bv \(\chi_{1476}(23, \cdot)\) n/a 1984 8
1476.2.bx \(\chi_{1476}(25, \cdot)\) n/a 336 8
1476.2.ca \(\chi_{1476}(19, \cdot)\) n/a 1648 16
1476.2.cb \(\chi_{1476}(17, \cdot)\) n/a 224 16
1476.2.cf \(\chi_{1476}(49, \cdot)\) n/a 672 16
1476.2.ch \(\chi_{1476}(131, \cdot)\) n/a 3968 16
1476.2.ck \(\chi_{1476}(29, \cdot)\) n/a 1344 32
1476.2.cl \(\chi_{1476}(7, \cdot)\) n/a 7936 32

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1476))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1476)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(369))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(492))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(738))\)\(^{\oplus 2}\)