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Properties

Label 2888.2
Level 2888
Weight 2
Dimension 144459
Nonzero newspaces 18
Sturm bound 1039680
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2888 = 2^{3} \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(1039680\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2888))\).

Total New Old
Modular forms 262944 146333 116611
Cusp forms 256897 144459 112438
Eisenstein series 6047 1874 4173

Trace form

\( 144459 q - 306 q^{2} - 306 q^{3} - 306 q^{4} - 306 q^{6} - 306 q^{7} - 306 q^{8} - 612 q^{9} + O(q^{10}) \) \( 144459 q - 306 q^{2} - 306 q^{3} - 306 q^{4} - 306 q^{6} - 306 q^{7} - 306 q^{8} - 612 q^{9} - 306 q^{10} - 306 q^{11} - 306 q^{12} - 306 q^{14} - 306 q^{15} - 306 q^{16} - 612 q^{17} - 306 q^{18} - 324 q^{19} - 594 q^{20} - 306 q^{22} - 306 q^{23} - 306 q^{24} - 612 q^{25} - 306 q^{26} - 288 q^{27} - 306 q^{28} + 36 q^{29} - 306 q^{30} - 270 q^{31} - 306 q^{32} - 504 q^{33} - 306 q^{34} - 234 q^{35} - 306 q^{36} + 36 q^{37} - 324 q^{38} - 486 q^{39} - 306 q^{40} - 576 q^{41} - 306 q^{42} - 234 q^{43} - 306 q^{44} + 108 q^{45} - 306 q^{46} - 270 q^{47} - 306 q^{48} - 576 q^{49} - 306 q^{50} - 288 q^{51} - 306 q^{52} - 414 q^{54} - 306 q^{55} - 306 q^{56} - 648 q^{57} - 594 q^{58} - 306 q^{59} - 378 q^{60} - 36 q^{61} - 486 q^{62} - 450 q^{63} - 594 q^{64} - 720 q^{65} - 594 q^{66} - 522 q^{67} - 558 q^{68} - 738 q^{70} - 414 q^{71} - 846 q^{72} - 774 q^{73} - 594 q^{74} - 594 q^{75} - 504 q^{76} - 108 q^{77} - 666 q^{78} - 558 q^{79} - 594 q^{80} - 774 q^{81} - 846 q^{82} - 414 q^{83} - 738 q^{84} - 558 q^{86} - 522 q^{87} - 594 q^{88} - 720 q^{89} - 594 q^{90} - 450 q^{91} - 486 q^{92} - 36 q^{93} - 378 q^{94} - 288 q^{95} - 594 q^{96} - 540 q^{97} - 306 q^{98} - 180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2888))\)

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
2888.2.a \(\chi_{2888}(1, \cdot)\) 2888.2.a.a 1 1
2888.2.a.b 1
2888.2.a.c 1
2888.2.a.d 1
2888.2.a.e 1
2888.2.a.f 1
2888.2.a.g 2
2888.2.a.h 2
2888.2.a.i 2
2888.2.a.j 2
2888.2.a.k 2
2888.2.a.l 2
2888.2.a.m 3
2888.2.a.n 3
2888.2.a.o 3
2888.2.a.p 3
2888.2.a.q 3
2888.2.a.r 3
2888.2.a.s 3
2888.2.a.t 6
2888.2.a.u 6
2888.2.a.v 8
2888.2.a.w 8
2888.2.a.x 9
2888.2.a.y 9
2888.2.b \(\chi_{2888}(1443, \cdot)\) n/a 324 1
2888.2.c \(\chi_{2888}(1445, \cdot)\) n/a 324 1
2888.2.h \(\chi_{2888}(2887, \cdot)\) None 0 1
2888.2.i \(\chi_{2888}(1873, \cdot)\) n/a 170 2
2888.2.j \(\chi_{2888}(791, \cdot)\) None 0 2
2888.2.o \(\chi_{2888}(2235, \cdot)\) n/a 648 2
2888.2.p \(\chi_{2888}(429, \cdot)\) n/a 648 2
2888.2.q \(\chi_{2888}(1137, \cdot)\) n/a 510 6
2888.2.t \(\chi_{2888}(245, \cdot)\) n/a 1944 6
2888.2.v \(\chi_{2888}(299, \cdot)\) n/a 1944 6
2888.2.w \(\chi_{2888}(127, \cdot)\) None 0 6
2888.2.y \(\chi_{2888}(153, \cdot)\) n/a 1710 18
2888.2.z \(\chi_{2888}(151, \cdot)\) None 0 18
2888.2.be \(\chi_{2888}(77, \cdot)\) n/a 6804 18
2888.2.bf \(\chi_{2888}(75, \cdot)\) n/a 6804 18
2888.2.bg \(\chi_{2888}(49, \cdot)\) n/a 3420 36
2888.2.bh \(\chi_{2888}(45, \cdot)\) n/a 13608 36
2888.2.bi \(\chi_{2888}(27, \cdot)\) n/a 13608 36
2888.2.bn \(\chi_{2888}(31, \cdot)\) None 0 36
2888.2.bo \(\chi_{2888}(9, \cdot)\) n/a 10260 108
2888.2.bq \(\chi_{2888}(15, \cdot)\) None 0 108
2888.2.br \(\chi_{2888}(3, \cdot)\) n/a 40824 108
2888.2.bt \(\chi_{2888}(5, \cdot)\) n/a 40824 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2888))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2888)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2888))\)\(^{\oplus 1}\)