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Properties

Label 1506.2
Level 1506
Weight 2
Dimension 15751
Nonzero newspaces 8
Sturm bound 252000
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1506 = 2 \cdot 3 \cdot 251 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(252000\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1506))\).

Total New Old
Modular forms 64000 15751 48249
Cusp forms 62001 15751 46250
Eisenstein series 1999 0 1999

Trace form

\( 15751 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 15751 q + q^{2} + q^{3} + q^{4} + 6 q^{5} + q^{6} + 8 q^{7} + q^{8} + q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + 14 q^{13} + 8 q^{14} + 6 q^{15} + q^{16} + 18 q^{17} + q^{18} + 20 q^{19} + 6 q^{20} + 8 q^{21} + 12 q^{22} + 24 q^{23} + q^{24} + 31 q^{25} + 14 q^{26} + q^{27} + 8 q^{28} + 30 q^{29} + 6 q^{30} + 32 q^{31} + q^{32} + 12 q^{33} + 18 q^{34} + 48 q^{35} + q^{36} + 38 q^{37} + 20 q^{38} + 14 q^{39} + 6 q^{40} + 42 q^{41} + 8 q^{42} + 44 q^{43} + 12 q^{44} + 6 q^{45} + 24 q^{46} + 48 q^{47} + q^{48} + 57 q^{49} + 31 q^{50} + 18 q^{51} + 14 q^{52} + 54 q^{53} + q^{54} + 72 q^{55} + 8 q^{56} + 20 q^{57} + 30 q^{58} + 60 q^{59} + 6 q^{60} + 62 q^{61} + 32 q^{62} + 8 q^{63} + q^{64} + 84 q^{65} + 12 q^{66} + 68 q^{67} + 18 q^{68} + 24 q^{69} + 48 q^{70} + 72 q^{71} + q^{72} + 74 q^{73} + 38 q^{74} + 31 q^{75} + 20 q^{76} + 96 q^{77} + 14 q^{78} + 80 q^{79} + 6 q^{80} + q^{81} + 42 q^{82} + 84 q^{83} + 8 q^{84} + 108 q^{85} + 44 q^{86} + 30 q^{87} + 12 q^{88} + 90 q^{89} + 6 q^{90} + 112 q^{91} + 24 q^{92} + 32 q^{93} + 48 q^{94} + 120 q^{95} + q^{96} + 98 q^{97} + 57 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1506))\)

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
1506.2.a \(\chi_{1506}(1, \cdot)\) 1506.2.a.a 1 1
1506.2.a.b 1
1506.2.a.c 1
1506.2.a.d 1
1506.2.a.e 1
1506.2.a.f 1
1506.2.a.g 1
1506.2.a.h 1
1506.2.a.i 2
1506.2.a.j 2
1506.2.a.k 4
1506.2.a.l 5
1506.2.a.m 5
1506.2.a.n 5
1506.2.a.o 6
1506.2.a.p 6
1506.2.c \(\chi_{1506}(1505, \cdot)\) 1506.2.c.a 42 1
1506.2.c.b 42
1506.2.e \(\chi_{1506}(271, \cdot)\) n/a 168 4
1506.2.f \(\chi_{1506}(353, \cdot)\) n/a 336 4
1506.2.i \(\chi_{1506}(25, \cdot)\) n/a 840 20
1506.2.k \(\chi_{1506}(47, \cdot)\) n/a 1680 20
1506.2.m \(\chi_{1506}(7, \cdot)\) n/a 4200 100
1506.2.p \(\chi_{1506}(11, \cdot)\) n/a 8400 100

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1506))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1506)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(502))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(753))\)\(^{\oplus 2}\)