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Properties

Label 1812.2
Level 1812
Weight 2
Dimension 39600
Nonzero newspaces 24
Sturm bound 364800
Trace bound 15

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Defining parameters

Level: \( N \) = \( 1812 = 2^{2} \cdot 3 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(364800\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1812))\).

Total New Old
Modular forms 92700 40192 52508
Cusp forms 89701 39600 50101
Eisenstein series 2999 592 2407

Trace form

\( 39600 q - 150 q^{4} - 75 q^{6} - 150 q^{9} + O(q^{10}) \) \( 39600 q - 150 q^{4} - 75 q^{6} - 150 q^{9} - 150 q^{10} - 75 q^{12} - 300 q^{13} - 150 q^{16} - 75 q^{18} - 150 q^{21} - 150 q^{22} - 75 q^{24} - 300 q^{25} - 150 q^{28} - 75 q^{30} - 150 q^{33} - 150 q^{34} - 75 q^{36} - 300 q^{37} - 150 q^{40} - 75 q^{42} - 150 q^{45} - 150 q^{46} - 75 q^{48} - 300 q^{49} - 150 q^{52} - 75 q^{54} - 150 q^{57} - 150 q^{58} - 75 q^{60} - 300 q^{61} - 150 q^{64} - 75 q^{66} - 150 q^{69} - 150 q^{70} - 75 q^{72} - 300 q^{73} - 150 q^{76} - 75 q^{78} - 150 q^{81} - 150 q^{82} - 75 q^{84} - 300 q^{85} - 150 q^{88} - 75 q^{90} - 150 q^{93} - 150 q^{94} - 75 q^{96} - 300 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1812))\)

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
1812.2.a \(\chi_{1812}(1, \cdot)\) 1812.2.a.a 1 1
1812.2.a.b 1
1812.2.a.c 2
1812.2.a.d 2
1812.2.a.e 3
1812.2.a.f 4
1812.2.a.g 5
1812.2.a.h 8
1812.2.b \(\chi_{1812}(905, \cdot)\) 1812.2.b.a 2 1
1812.2.b.b 48
1812.2.c \(\chi_{1812}(1511, \cdot)\) n/a 300 1
1812.2.h \(\chi_{1812}(1207, \cdot)\) n/a 152 1
1812.2.i \(\chi_{1812}(1477, \cdot)\) 1812.2.i.a 2 2
1812.2.i.b 2
1812.2.i.c 2
1812.2.i.d 2
1812.2.i.e 20
1812.2.i.f 22
1812.2.j \(\chi_{1812}(361, \cdot)\) n/a 104 4
1812.2.k \(\chi_{1812}(1327, \cdot)\) n/a 304 2
1812.2.p \(\chi_{1812}(1175, \cdot)\) n/a 600 2
1812.2.q \(\chi_{1812}(1025, \cdot)\) n/a 102 2
1812.2.r \(\chi_{1812}(283, \cdot)\) n/a 608 4
1812.2.w \(\chi_{1812}(59, \cdot)\) n/a 1200 4
1812.2.x \(\chi_{1812}(389, \cdot)\) n/a 200 4
1812.2.y \(\chi_{1812}(85, \cdot)\) n/a 200 8
1812.2.z \(\chi_{1812}(229, \cdot)\) n/a 520 20
1812.2.ba \(\chi_{1812}(113, \cdot)\) n/a 408 8
1812.2.bb \(\chi_{1812}(155, \cdot)\) n/a 2400 8
1812.2.bg \(\chi_{1812}(415, \cdot)\) n/a 1216 8
1812.2.bh \(\chi_{1812}(41, \cdot)\) n/a 1000 20
1812.2.bk \(\chi_{1812}(275, \cdot)\) n/a 6000 20
1812.2.bl \(\chi_{1812}(67, \cdot)\) n/a 3040 20
1812.2.bo \(\chi_{1812}(25, \cdot)\) n/a 1000 40
1812.2.br \(\chi_{1812}(77, \cdot)\) n/a 2040 40
1812.2.bu \(\chi_{1812}(11, \cdot)\) n/a 12000 40
1812.2.bv \(\chi_{1812}(7, \cdot)\) n/a 6080 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1812))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1812)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(302))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(453))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(604))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(906))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1812))\)\(^{\oplus 1}\)