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Properties

Label 1208.2
Level 1208
Weight 2
Dimension 25350
Nonzero newspaces 18
Sturm bound 182400
Trace bound 8

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Defining parameters

Level: \( N \) = \( 1208 = 2^{3} \cdot 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(182400\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1208))\).

Total New Old
Modular forms 46500 25946 20554
Cusp forms 44701 25350 19351
Eisenstein series 1799 596 1203

Trace form

\( 25350 q - 150 q^{2} - 150 q^{3} - 150 q^{4} - 150 q^{6} - 150 q^{7} - 150 q^{8} - 300 q^{9} + O(q^{10}) \) \( 25350 q - 150 q^{2} - 150 q^{3} - 150 q^{4} - 150 q^{6} - 150 q^{7} - 150 q^{8} - 300 q^{9} - 150 q^{10} - 150 q^{11} - 150 q^{12} - 150 q^{14} - 150 q^{15} - 150 q^{16} - 300 q^{17} - 150 q^{18} - 150 q^{19} - 150 q^{20} - 150 q^{22} - 150 q^{23} - 150 q^{24} - 300 q^{25} - 150 q^{26} - 150 q^{27} - 150 q^{28} - 150 q^{30} - 150 q^{31} - 150 q^{32} - 300 q^{33} - 150 q^{34} - 150 q^{35} - 150 q^{36} - 150 q^{38} - 150 q^{39} - 150 q^{40} - 300 q^{41} - 150 q^{42} - 150 q^{43} - 150 q^{44} - 150 q^{46} - 150 q^{47} - 150 q^{48} - 300 q^{49} - 150 q^{50} - 150 q^{51} - 150 q^{52} - 150 q^{54} - 150 q^{55} - 150 q^{56} - 300 q^{57} - 150 q^{58} - 150 q^{59} - 150 q^{60} - 150 q^{62} - 150 q^{63} - 150 q^{64} - 300 q^{65} - 150 q^{66} - 150 q^{67} - 150 q^{68} - 150 q^{70} - 150 q^{71} - 150 q^{72} - 300 q^{73} - 150 q^{74} - 150 q^{75} - 150 q^{76} - 150 q^{78} - 150 q^{79} - 150 q^{80} - 300 q^{81} - 150 q^{82} - 150 q^{83} - 150 q^{84} - 150 q^{86} - 150 q^{87} - 150 q^{88} - 300 q^{89} - 150 q^{90} - 150 q^{91} - 150 q^{92} - 150 q^{94} - 150 q^{95} - 150 q^{96} - 300 q^{97} - 150 q^{98} - 150 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1208))\)

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
1208.2.a \(\chi_{1208}(1, \cdot)\) 1208.2.a.a 1 1
1208.2.a.b 3
1208.2.a.c 4
1208.2.a.d 8
1208.2.a.e 11
1208.2.a.f 11
1208.2.b \(\chi_{1208}(605, \cdot)\) n/a 150 1
1208.2.c \(\chi_{1208}(603, \cdot)\) n/a 150 1
1208.2.h \(\chi_{1208}(1207, \cdot)\) None 0 1
1208.2.i \(\chi_{1208}(873, \cdot)\) 1208.2.i.a 38 2
1208.2.i.b 38
1208.2.j \(\chi_{1208}(321, \cdot)\) n/a 152 4
1208.2.m \(\chi_{1208}(723, \cdot)\) n/a 300 2
1208.2.n \(\chi_{1208}(269, \cdot)\) n/a 300 2
1208.2.o \(\chi_{1208}(119, \cdot)\) None 0 2
1208.2.r \(\chi_{1208}(87, \cdot)\) None 0 4
1208.2.w \(\chi_{1208}(243, \cdot)\) n/a 600 4
1208.2.x \(\chi_{1208}(461, \cdot)\) n/a 600 4
1208.2.y \(\chi_{1208}(105, \cdot)\) n/a 304 8
1208.2.z \(\chi_{1208}(9, \cdot)\) n/a 760 20
1208.2.bc \(\chi_{1208}(23, \cdot)\) None 0 8
1208.2.bd \(\chi_{1208}(85, \cdot)\) n/a 1200 8
1208.2.be \(\chi_{1208}(75, \cdot)\) n/a 1200 8
1208.2.bh \(\chi_{1208}(3, \cdot)\) n/a 3000 20
1208.2.bk \(\chi_{1208}(79, \cdot)\) None 0 20
1208.2.bl \(\chi_{1208}(29, \cdot)\) n/a 3000 20
1208.2.bo \(\chi_{1208}(17, \cdot)\) n/a 1520 40
1208.2.br \(\chi_{1208}(35, \cdot)\) n/a 6000 40
1208.2.bu \(\chi_{1208}(5, \cdot)\) n/a 6000 40
1208.2.bv \(\chi_{1208}(7, \cdot)\) None 0 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1208))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1208)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(302))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(604))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1208))\)\(^{\oplus 1}\)