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Properties

Label 2028.4
Level 2028
Weight 4
Dimension 146891
Nonzero newspaces 24
Sturm bound 908544
Trace bound 6

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Defining parameters

Level: \( N \) = \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(908544\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2028))\).

Total New Old
Modular forms 342984 147711 195273
Cusp forms 338424 146891 191533
Eisenstein series 4560 820 3740

Trace form

\( 146891 q + 3 q^{3} - 140 q^{4} - 18 q^{5} - 90 q^{6} - 136 q^{7} - 135 q^{9} + O(q^{10}) \) \( 146891 q + 3 q^{3} - 140 q^{4} - 18 q^{5} - 90 q^{6} - 136 q^{7} - 135 q^{9} - 52 q^{10} + 276 q^{11} + 66 q^{12} + 90 q^{15} - 356 q^{16} + 390 q^{17} + 810 q^{18} - 244 q^{19} + 480 q^{20} - 468 q^{21} - 1452 q^{22} - 840 q^{23} - 1986 q^{24} - 1337 q^{25} - 1500 q^{26} - 1629 q^{27} - 2652 q^{28} - 1014 q^{29} - 786 q^{30} + 224 q^{31} + 2040 q^{32} + 696 q^{33} + 4700 q^{34} + 2976 q^{35} + 3018 q^{36} + 274 q^{37} - 492 q^{39} - 7708 q^{40} + 7878 q^{41} - 2310 q^{42} + 1796 q^{43} - 600 q^{44} + 582 q^{45} + 4236 q^{46} - 1056 q^{47} + 3198 q^{48} - 13091 q^{49} + 10584 q^{50} - 2394 q^{51} + 5364 q^{52} - 9906 q^{53} + 822 q^{54} - 6264 q^{55} + 6696 q^{56} - 4224 q^{57} + 236 q^{58} + 2004 q^{59} - 5046 q^{60} + 7906 q^{61} - 7080 q^{62} - 456 q^{63} - 13820 q^{64} + 11718 q^{65} - 13158 q^{66} + 8924 q^{67} + 5484 q^{69} - 2652 q^{70} + 696 q^{71} + 6306 q^{72} - 902 q^{73} + 2157 q^{75} + 2028 q^{76} - 12960 q^{77} + 8706 q^{78} - 10528 q^{79} - 1647 q^{81} - 1252 q^{82} + 1260 q^{83} + 1458 q^{84} + 3904 q^{85} - 19488 q^{86} + 3666 q^{87} - 19452 q^{88} + 2682 q^{89} - 24942 q^{90} + 4680 q^{91} - 4176 q^{92} - 4404 q^{93} + 1020 q^{94} + 8520 q^{95} + 930 q^{96} + 17938 q^{97} + 15768 q^{98} + 7164 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2028))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2028.4.a \(\chi_{2028}(1, \cdot)\) 2028.4.a.a 1 1
2028.4.a.b 1
2028.4.a.c 1
2028.4.a.d 2
2028.4.a.e 2
2028.4.a.f 2
2028.4.a.g 2
2028.4.a.h 2
2028.4.a.i 2
2028.4.a.j 4
2028.4.a.k 4
2028.4.a.l 4
2028.4.a.m 4
2028.4.a.n 4
2028.4.a.o 6
2028.4.a.p 9
2028.4.a.q 9
2028.4.a.r 9
2028.4.a.s 9
2028.4.b \(\chi_{2028}(337, \cdot)\) 2028.4.b.a 2 1
2028.4.b.b 2
2028.4.b.c 2
2028.4.b.d 2
2028.4.b.e 4
2028.4.b.f 4
2028.4.b.g 4
2028.4.b.h 6
2028.4.b.i 8
2028.4.b.j 8
2028.4.b.k 18
2028.4.b.l 18
2028.4.c \(\chi_{2028}(1691, \cdot)\) n/a 908 1
2028.4.h \(\chi_{2028}(2027, \cdot)\) n/a 904 1
2028.4.i \(\chi_{2028}(529, \cdot)\) n/a 152 2
2028.4.k \(\chi_{2028}(775, \cdot)\) n/a 924 2
2028.4.m \(\chi_{2028}(437, \cdot)\) n/a 308 2
2028.4.p \(\chi_{2028}(191, \cdot)\) n/a 1808 2
2028.4.q \(\chi_{2028}(361, \cdot)\) n/a 156 2
2028.4.r \(\chi_{2028}(23, \cdot)\) n/a 1808 2
2028.4.u \(\chi_{2028}(89, \cdot)\) n/a 616 4
2028.4.w \(\chi_{2028}(19, \cdot)\) n/a 1848 4
2028.4.y \(\chi_{2028}(157, \cdot)\) n/a 1104 12
2028.4.z \(\chi_{2028}(155, \cdot)\) n/a 13056 12
2028.4.be \(\chi_{2028}(131, \cdot)\) n/a 13056 12
2028.4.bf \(\chi_{2028}(25, \cdot)\) n/a 1080 12
2028.4.bg \(\chi_{2028}(61, \cdot)\) n/a 2208 24
2028.4.bi \(\chi_{2028}(5, \cdot)\) n/a 4368 24
2028.4.bk \(\chi_{2028}(31, \cdot)\) n/a 13104 24
2028.4.bn \(\chi_{2028}(95, \cdot)\) n/a 26112 24
2028.4.bo \(\chi_{2028}(49, \cdot)\) n/a 2160 24
2028.4.bp \(\chi_{2028}(35, \cdot)\) n/a 26112 24
2028.4.bs \(\chi_{2028}(7, \cdot)\) n/a 26208 48
2028.4.bu \(\chi_{2028}(41, \cdot)\) n/a 8736 48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2028))\) into lower level spaces

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