Properties

Label 2028.2
Level 2028
Weight 2
Dimension 48690
Nonzero newspaces 24
Sturm bound 454272
Trace bound 12

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(454272\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2028))\).

Total New Old
Modular forms 115848 49510 66338
Cusp forms 111289 48690 62599
Eisenstein series 4559 820 3739

Trace form

\( 48690q - 132q^{4} - 66q^{6} - 8q^{7} - 136q^{9} + O(q^{10}) \) \( 48690q - 132q^{4} - 66q^{6} - 8q^{7} - 136q^{9} - 132q^{10} - 24q^{11} - 54q^{12} - 312q^{13} - 24q^{15} - 132q^{16} - 12q^{17} - 30q^{18} + 16q^{19} + 96q^{20} - 88q^{21} - 12q^{22} + 48q^{23} + 30q^{24} - 156q^{25} + 60q^{26} + 72q^{27} - 12q^{28} + 60q^{29} + 30q^{30} + 48q^{31} + 120q^{32} - 48q^{33} - 36q^{34} + 48q^{35} - 30q^{36} - 252q^{37} + 28q^{39} - 348q^{40} + 132q^{41} - 102q^{42} + 64q^{43} - 120q^{44} - 36q^{45} - 372q^{46} + 48q^{47} - 162q^{48} + 40q^{49} - 216q^{50} + 48q^{51} - 252q^{52} + 96q^{53} - 42q^{54} + 24q^{55} - 216q^{56} - 40q^{57} - 324q^{58} - 24q^{59} - 246q^{60} - 132q^{61} - 120q^{62} - 124q^{63} - 252q^{64} + 18q^{65} - 294q^{66} - 80q^{67} - 288q^{69} - 252q^{70} - 48q^{71} - 222q^{72} - 344q^{73} - 208q^{75} - 132q^{76} - 144q^{77} - 186q^{78} - 144q^{79} - 256q^{81} - 132q^{82} - 72q^{83} - 318q^{84} - 420q^{85} - 96q^{86} - 168q^{87} - 252q^{88} - 144q^{89} - 366q^{90} - 52q^{91} - 144q^{92} - 304q^{93} - 324q^{94} - 96q^{95} - 318q^{96} - 432q^{97} - 216q^{98} + 36q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2028))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2028.2.a \(\chi_{2028}(1, \cdot)\) 2028.2.a.a 1 1
2028.2.a.b 1
2028.2.a.c 1
2028.2.a.d 1
2028.2.a.e 1
2028.2.a.f 1
2028.2.a.g 2
2028.2.a.h 2
2028.2.a.i 3
2028.2.a.j 3
2028.2.a.k 3
2028.2.a.l 3
2028.2.a.m 4
2028.2.b \(\chi_{2028}(337, \cdot)\) 2028.2.b.a 2 1
2028.2.b.b 2
2028.2.b.c 2
2028.2.b.d 2
2028.2.b.e 4
2028.2.b.f 6
2028.2.b.g 6
2028.2.c \(\chi_{2028}(1691, \cdot)\) n/a 288 1
2028.2.h \(\chi_{2028}(2027, \cdot)\) n/a 288 1
2028.2.i \(\chi_{2028}(529, \cdot)\) 2028.2.i.a 2 2
2028.2.i.b 2
2028.2.i.c 2
2028.2.i.d 2
2028.2.i.e 2
2028.2.i.f 2
2028.2.i.g 2
2028.2.i.h 4
2028.2.i.i 4
2028.2.i.j 6
2028.2.i.k 6
2028.2.i.l 6
2028.2.i.m 6
2028.2.i.n 8
2028.2.k \(\chi_{2028}(775, \cdot)\) n/a 308 2
2028.2.m \(\chi_{2028}(437, \cdot)\) n/a 104 2
2028.2.p \(\chi_{2028}(191, \cdot)\) n/a 576 2
2028.2.q \(\chi_{2028}(361, \cdot)\) 2028.2.q.a 2 2
2028.2.q.b 2
2028.2.q.c 2
2028.2.q.d 4
2028.2.q.e 4
2028.2.q.f 4
2028.2.q.g 4
2028.2.q.h 4
2028.2.q.i 12
2028.2.q.j 12
2028.2.r \(\chi_{2028}(23, \cdot)\) n/a 576 2
2028.2.u \(\chi_{2028}(89, \cdot)\) n/a 204 4
2028.2.w \(\chi_{2028}(19, \cdot)\) n/a 616 4
2028.2.y \(\chi_{2028}(157, \cdot)\) n/a 360 12
2028.2.z \(\chi_{2028}(155, \cdot)\) n/a 4320 12
2028.2.be \(\chi_{2028}(131, \cdot)\) n/a 4320 12
2028.2.bf \(\chi_{2028}(25, \cdot)\) n/a 384 12
2028.2.bg \(\chi_{2028}(61, \cdot)\) n/a 696 24
2028.2.bi \(\chi_{2028}(5, \cdot)\) n/a 1440 24
2028.2.bk \(\chi_{2028}(31, \cdot)\) n/a 4368 24
2028.2.bn \(\chi_{2028}(95, \cdot)\) n/a 8640 24
2028.2.bo \(\chi_{2028}(49, \cdot)\) n/a 744 24
2028.2.bp \(\chi_{2028}(35, \cdot)\) n/a 8640 24
2028.2.bs \(\chi_{2028}(7, \cdot)\) n/a 8736 48
2028.2.bu \(\chi_{2028}(41, \cdot)\) n/a 2928 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2028))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2028)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 2}\)