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Properties

Label 2151.4
Level 2151
Weight 4
Dimension 405899
Nonzero newspaces 16
Sturm bound 1370880
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(1370880\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2151))\).

Total New Old
Modular forms 515984 408031 107953
Cusp forms 512176 405899 106277
Eisenstein series 3808 2132 1676

Trace form

\( 405899 q - 351 q^{2} - 470 q^{3} - 331 q^{4} - 327 q^{5} - 494 q^{6} - 383 q^{7} - 489 q^{8} - 566 q^{9} + O(q^{10}) \) \( 405899 q - 351 q^{2} - 470 q^{3} - 331 q^{4} - 327 q^{5} - 494 q^{6} - 383 q^{7} - 489 q^{8} - 566 q^{9} - 1095 q^{10} - 225 q^{11} - 164 q^{12} - 239 q^{13} - 237 q^{14} - 530 q^{15} - 499 q^{16} - 753 q^{17} - 908 q^{18} - 875 q^{19} - 381 q^{20} - 518 q^{21} - 423 q^{22} - 291 q^{23} - 278 q^{24} - 349 q^{25} + 699 q^{26} + 388 q^{27} - 1415 q^{28} - 459 q^{29} - 1052 q^{30} - 887 q^{31} - 1203 q^{32} - 872 q^{33} + 237 q^{34} - 369 q^{35} - 26 q^{36} - 1091 q^{37} - 1479 q^{38} - 1994 q^{39} + 171 q^{40} - 93 q^{41} + 496 q^{42} + 859 q^{43} + 567 q^{44} + 874 q^{45} - 15 q^{46} + 441 q^{47} - 434 q^{48} - 1497 q^{49} - 1215 q^{50} - 1070 q^{51} - 3017 q^{52} - 573 q^{53} - 2906 q^{54} - 3579 q^{55} - 225 q^{56} + 1966 q^{57} - 477 q^{58} + 1239 q^{59} - 404 q^{60} + 157 q^{61} - 813 q^{62} - 1682 q^{63} + 2861 q^{64} - 27 q^{65} + 1504 q^{66} + 3379 q^{67} + 1029 q^{68} - 2258 q^{69} + 279 q^{70} - 5829 q^{71} - 2258 q^{72} - 1631 q^{73} + 1275 q^{74} + 250 q^{75} - 2519 q^{76} - 687 q^{77} + 1504 q^{78} - 3731 q^{79} - 741 q^{80} + 658 q^{81} - 8331 q^{82} + 1269 q^{83} - 1760 q^{84} + 831 q^{85} - 291 q^{86} - 170 q^{87} + 2085 q^{88} + 1227 q^{89} + 1036 q^{90} + 4853 q^{91} - 2073 q^{92} - 50 q^{93} + 3843 q^{94} - 621 q^{95} - 2636 q^{96} + 3775 q^{97} + 1335 q^{98} - 1070 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2151))\)

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
2151.4.a \(\chi_{2151}(1, \cdot)\) 2151.4.a.a 22 1
2151.4.a.b 28
2151.4.a.c 28
2151.4.a.d 32
2151.4.a.e 32
2151.4.a.f 37
2151.4.a.g 59
2151.4.a.h 59
2151.4.b \(\chi_{2151}(2150, \cdot)\) n/a 240 1
2151.4.e \(\chi_{2151}(718, \cdot)\) n/a 1428 2
2151.4.h \(\chi_{2151}(716, \cdot)\) n/a 1436 2
2151.4.i \(\chi_{2151}(10, \cdot)\) n/a 1794 6
2151.4.l \(\chi_{2151}(215, \cdot)\) n/a 1440 6
2151.4.m \(\chi_{2151}(163, \cdot)\) n/a 4784 16
2151.4.n \(\chi_{2151}(283, \cdot)\) n/a 8616 12
2151.4.q \(\chi_{2151}(107, \cdot)\) n/a 3840 16
2151.4.r \(\chi_{2151}(38, \cdot)\) n/a 8616 12
2151.4.u \(\chi_{2151}(22, \cdot)\) n/a 22976 32
2151.4.v \(\chi_{2151}(23, \cdot)\) n/a 22976 32
2151.4.y \(\chi_{2151}(55, \cdot)\) n/a 28704 96
2151.4.z \(\chi_{2151}(26, \cdot)\) n/a 23040 96
2151.4.bc \(\chi_{2151}(4, \cdot)\) n/a 137856 192
2151.4.bf \(\chi_{2151}(14, \cdot)\) n/a 137856 192

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2151))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2151)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(239))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(717))\)\(^{\oplus 2}\)