↑

Properties

Label 2259.2
Level 2259
Weight 2
Dimension 148500
Nonzero newspaces 16
Sturm bound 756000
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2259 = 3^{2} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(756000\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2259))\).

Total New Old
Modular forms 191000 150740 40260
Cusp forms 187001 148500 38501
Eisenstein series 3999 2240 1759

Trace form

\( 148500 q - 375 q^{2} - 500 q^{3} - 375 q^{4} - 375 q^{5} - 500 q^{6} - 375 q^{7} - 375 q^{8} - 500 q^{9} + O(q^{10}) \) \( 148500 q - 375 q^{2} - 500 q^{3} - 375 q^{4} - 375 q^{5} - 500 q^{6} - 375 q^{7} - 375 q^{8} - 500 q^{9} - 1125 q^{10} - 375 q^{11} - 500 q^{12} - 375 q^{13} - 375 q^{14} - 500 q^{15} - 375 q^{16} - 375 q^{17} - 500 q^{18} - 1125 q^{19} - 375 q^{20} - 500 q^{21} - 375 q^{22} - 375 q^{23} - 500 q^{24} - 375 q^{25} - 375 q^{26} - 500 q^{27} - 1125 q^{28} - 375 q^{29} - 500 q^{30} - 375 q^{31} - 375 q^{32} - 500 q^{33} - 375 q^{34} - 375 q^{35} - 500 q^{36} - 1125 q^{37} - 375 q^{38} - 500 q^{39} - 375 q^{40} - 375 q^{41} - 500 q^{42} - 375 q^{43} - 375 q^{44} - 500 q^{45} - 1125 q^{46} - 375 q^{47} - 500 q^{48} - 375 q^{49} - 375 q^{50} - 500 q^{51} - 375 q^{52} - 375 q^{53} - 500 q^{54} - 1125 q^{55} - 375 q^{56} - 500 q^{57} - 375 q^{58} - 375 q^{59} - 500 q^{60} - 375 q^{61} - 375 q^{62} - 500 q^{63} - 1125 q^{64} - 375 q^{65} - 500 q^{66} - 375 q^{67} - 375 q^{68} - 500 q^{69} - 375 q^{70} - 375 q^{71} - 500 q^{72} - 1125 q^{73} - 375 q^{74} - 500 q^{75} - 375 q^{76} - 375 q^{77} - 500 q^{78} - 375 q^{79} - 375 q^{80} - 500 q^{81} - 1125 q^{82} - 375 q^{83} - 500 q^{84} - 375 q^{85} - 375 q^{86} - 500 q^{87} - 375 q^{88} - 375 q^{89} - 500 q^{90} - 1125 q^{91} - 375 q^{92} - 500 q^{93} - 375 q^{94} - 375 q^{95} - 500 q^{96} - 375 q^{97} - 375 q^{98} - 500 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2259))\)

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
2259.2.a \(\chi_{2259}(1, \cdot)\) 2259.2.a.a 1 1
2259.2.a.b 1
2259.2.a.c 1
2259.2.a.d 2
2259.2.a.e 4
2259.2.a.f 4
2259.2.a.g 6
2259.2.a.h 6
2259.2.a.i 9
2259.2.a.j 11
2259.2.a.k 17
2259.2.a.l 21
2259.2.a.m 21
2259.2.d \(\chi_{2259}(2258, \cdot)\) 2259.2.d.a 84 1
2259.2.e \(\chi_{2259}(754, \cdot)\) n/a 500 2
2259.2.f \(\chi_{2259}(271, \cdot)\) n/a 416 4
2259.2.g \(\chi_{2259}(752, \cdot)\) n/a 500 2
2259.2.l \(\chi_{2259}(1106, \cdot)\) n/a 336 4
2259.2.m \(\chi_{2259}(364, \cdot)\) n/a 2000 8
2259.2.n \(\chi_{2259}(64, \cdot)\) n/a 2080 20
2259.2.o \(\chi_{2259}(32, \cdot)\) n/a 2000 8
2259.2.r \(\chi_{2259}(8, \cdot)\) n/a 1680 20
2259.2.u \(\chi_{2259}(4, \cdot)\) n/a 10000 40
2259.2.v \(\chi_{2259}(28, \cdot)\) n/a 10400 100
2259.2.y \(\chi_{2259}(2, \cdot)\) n/a 10000 40
2259.2.ba \(\chi_{2259}(26, \cdot)\) n/a 8400 100
2259.2.bc \(\chi_{2259}(7, \cdot)\) n/a 50000 200
2259.2.be \(\chi_{2259}(11, \cdot)\) n/a 50000 200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2259))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2259)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(753))\)\(^{\oplus 2}\)