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Properties

Label 1062.2
Level 1062
Weight 2
Dimension 8261
Nonzero newspaces 8
Sturm bound 125280
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1062 = 2 \cdot 3^{2} \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(125280\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1062))\).

Total New Old
Modular forms 32248 8261 23987
Cusp forms 30393 8261 22132
Eisenstein series 1855 0 1855

Trace form

\( 8261 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} + O(q^{10}) \) \( 8261 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} - 6 q^{11} + 4 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + 12 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{24} - 10 q^{25} - 8 q^{26} - 8 q^{28} + 12 q^{29} - 8 q^{31} + 2 q^{32} + 18 q^{33} - 6 q^{34} - 6 q^{36} + 16 q^{37} - 2 q^{38} + 18 q^{41} - 2 q^{43} + 12 q^{44} + 82 q^{46} + 46 q^{47} - 6 q^{48} + 110 q^{49} + 106 q^{50} - 18 q^{51} + 62 q^{52} + 68 q^{53} - 18 q^{54} + 174 q^{55} + 4 q^{56} - 6 q^{57} + 70 q^{58} + 119 q^{59} + 132 q^{61} + 74 q^{62} + 24 q^{63} - 4 q^{64} + 174 q^{65} + 126 q^{67} + 52 q^{68} + 116 q^{70} + 164 q^{71} - 6 q^{72} + 14 q^{73} + 50 q^{74} + 30 q^{75} - 2 q^{76} - 12 q^{77} + 12 q^{78} - 8 q^{79} + 18 q^{81} - 36 q^{82} + 24 q^{83} + 12 q^{84} - 2 q^{86} - 36 q^{87} - 6 q^{88} - 24 q^{89} - 16 q^{91} - 12 q^{92} - 12 q^{94} + 10 q^{97} + 12 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1062))\)

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
1062.2.a \(\chi_{1062}(1, \cdot)\) 1062.2.a.a 1 1
1062.2.a.b 1
1062.2.a.c 1
1062.2.a.d 1
1062.2.a.e 1
1062.2.a.f 1
1062.2.a.g 1
1062.2.a.h 1
1062.2.a.i 1
1062.2.a.j 1
1062.2.a.k 1
1062.2.a.l 1
1062.2.a.m 2
1062.2.a.n 3
1062.2.a.o 4
1062.2.a.p 4
1062.2.c \(\chi_{1062}(1061, \cdot)\) 1062.2.c.a 2 1
1062.2.c.b 2
1062.2.c.c 4
1062.2.c.d 4
1062.2.c.e 4
1062.2.c.f 4
1062.2.e \(\chi_{1062}(355, \cdot)\) 1062.2.e.a 6 2
1062.2.e.b 6
1062.2.e.c 6
1062.2.e.d 14
1062.2.e.e 26
1062.2.e.f 26
1062.2.e.g 32
1062.2.g \(\chi_{1062}(353, \cdot)\) n/a 120 2
1062.2.i \(\chi_{1062}(19, \cdot)\) n/a 700 28
1062.2.k \(\chi_{1062}(89, \cdot)\) n/a 560 28
1062.2.m \(\chi_{1062}(7, \cdot)\) n/a 3360 56
1062.2.o \(\chi_{1062}(11, \cdot)\) n/a 3360 56

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1062))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1062)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(354))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(531))\)\(^{\oplus 2}\)