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Properties

Label 2151.2
Level 2151
Weight 2
Dimension 134589
Nonzero newspaces 16
Sturm bound 685440
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(685440\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2151))\).

Total New Old
Modular forms 173264 136721 36543
Cusp forms 169457 134589 34868
Eisenstein series 3807 2132 1675

Trace form

\( 134589 q - 357 q^{2} - 476 q^{3} - 357 q^{4} - 357 q^{5} - 476 q^{6} - 357 q^{7} - 357 q^{8} - 476 q^{9} + O(q^{10}) \) \( 134589 q - 357 q^{2} - 476 q^{3} - 357 q^{4} - 357 q^{5} - 476 q^{6} - 357 q^{7} - 357 q^{8} - 476 q^{9} - 1071 q^{10} - 357 q^{11} - 476 q^{12} - 357 q^{13} - 357 q^{14} - 476 q^{15} - 357 q^{16} - 357 q^{17} - 476 q^{18} - 1071 q^{19} - 357 q^{20} - 476 q^{21} - 357 q^{22} - 357 q^{23} - 476 q^{24} - 357 q^{25} - 357 q^{26} - 476 q^{27} - 1071 q^{28} - 357 q^{29} - 476 q^{30} - 357 q^{31} - 357 q^{32} - 476 q^{33} - 357 q^{34} - 357 q^{35} - 476 q^{36} - 1071 q^{37} - 357 q^{38} - 476 q^{39} - 357 q^{40} - 357 q^{41} - 476 q^{42} - 357 q^{43} - 357 q^{44} - 476 q^{45} - 1071 q^{46} - 357 q^{47} - 476 q^{48} - 357 q^{49} - 357 q^{50} - 476 q^{51} - 357 q^{52} - 357 q^{53} - 476 q^{54} - 1071 q^{55} - 357 q^{56} - 476 q^{57} - 357 q^{58} - 357 q^{59} - 476 q^{60} - 357 q^{61} - 357 q^{62} - 476 q^{63} - 1071 q^{64} - 357 q^{65} - 476 q^{66} - 357 q^{67} - 357 q^{68} - 476 q^{69} - 357 q^{70} - 357 q^{71} - 476 q^{72} - 1071 q^{73} - 357 q^{74} - 476 q^{75} - 357 q^{76} - 357 q^{77} - 476 q^{78} - 357 q^{79} - 357 q^{80} - 476 q^{81} - 1071 q^{82} - 357 q^{83} - 476 q^{84} - 357 q^{85} - 357 q^{86} - 476 q^{87} - 357 q^{88} - 357 q^{89} - 476 q^{90} - 1071 q^{91} - 357 q^{92} - 476 q^{93} - 357 q^{94} - 357 q^{95} - 476 q^{96} - 357 q^{97} - 357 q^{98} - 476 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2151))\)

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
2151.2.a \(\chi_{2151}(1, \cdot)\) 2151.2.a.a 2 1
2151.2.a.b 2
2151.2.a.c 2
2151.2.a.d 3
2151.2.a.e 6
2151.2.a.f 7
2151.2.a.g 8
2151.2.a.h 12
2151.2.a.i 17
2151.2.a.j 20
2151.2.a.k 20
2151.2.b \(\chi_{2151}(2150, \cdot)\) 2151.2.b.a 80 1
2151.2.e \(\chi_{2151}(718, \cdot)\) n/a 476 2
2151.2.h \(\chi_{2151}(716, \cdot)\) n/a 476 2
2151.2.i \(\chi_{2151}(10, \cdot)\) n/a 594 6
2151.2.l \(\chi_{2151}(215, \cdot)\) n/a 480 6
2151.2.m \(\chi_{2151}(163, \cdot)\) n/a 1584 16
2151.2.n \(\chi_{2151}(283, \cdot)\) n/a 2856 12
2151.2.q \(\chi_{2151}(107, \cdot)\) n/a 1280 16
2151.2.r \(\chi_{2151}(38, \cdot)\) n/a 2856 12
2151.2.u \(\chi_{2151}(22, \cdot)\) n/a 7616 32
2151.2.v \(\chi_{2151}(23, \cdot)\) n/a 7616 32
2151.2.y \(\chi_{2151}(55, \cdot)\) n/a 9504 96
2151.2.z \(\chi_{2151}(26, \cdot)\) n/a 7680 96
2151.2.bc \(\chi_{2151}(4, \cdot)\) n/a 45696 192
2151.2.bf \(\chi_{2151}(14, \cdot)\) n/a 45696 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2151))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2151)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(239))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(717))\)\(^{\oplus 2}\)