↑

Properties

Label 228.6
Level 228
Weight 6
Dimension 3098
Nonzero newspaces 12
Sturm bound 17280
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(17280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(228))\).

Total New Old
Modular forms 7380 3162 4218
Cusp forms 7020 3098 3922
Eisenstein series 360 64 296

Trace form

\( 3098 q - 34 q^{4} - 57 q^{6} + 30 q^{9} + O(q^{10}) \) \( 3098 q - 34 q^{4} - 57 q^{6} + 30 q^{9} + 526 q^{10} + 1383 q^{12} - 4604 q^{13} - 1782 q^{15} - 4690 q^{16} + 4302 q^{17} - 7410 q^{18} + 12810 q^{19} - 291 q^{21} + 16590 q^{22} - 10278 q^{23} + 22455 q^{24} - 20664 q^{25} - 21474 q^{27} - 67728 q^{28} + 22716 q^{29} + 19842 q^{30} + 39276 q^{31} + 67590 q^{32} + 4440 q^{33} + 44104 q^{34} - 59112 q^{35} - 22875 q^{36} - 62252 q^{37} - 167706 q^{38} - 57726 q^{39} - 183392 q^{40} + 1116 q^{41} - 49695 q^{42} + 107928 q^{43} + 191790 q^{44} + 162399 q^{45} + 364272 q^{46} + 68076 q^{47} + 180120 q^{48} - 27832 q^{49} - 308394 q^{50} - 72306 q^{51} - 168434 q^{52} - 156249 q^{54} - 181917 q^{57} + 125116 q^{58} + 374262 q^{60} - 645896 q^{61} + 87390 q^{62} + 119142 q^{63} - 724354 q^{64} + 569700 q^{65} - 435441 q^{66} + 308088 q^{67} - 374346 q^{68} + 431565 q^{69} + 120246 q^{70} - 68004 q^{71} + 138237 q^{72} - 465614 q^{73} + 756720 q^{74} - 236250 q^{75} + 1085058 q^{76} - 856854 q^{77} + 532533 q^{78} - 99744 q^{79} + 147600 q^{80} - 615078 q^{81} - 1100288 q^{82} - 286110 q^{83} - 1069581 q^{84} + 1429844 q^{85} - 1156806 q^{86} + 131076 q^{87} - 896130 q^{88} + 748494 q^{89} + 494610 q^{90} + 236568 q^{91} + 1099890 q^{92} + 319332 q^{93} + 572520 q^{94} + 472014 q^{95} + 21558 q^{96} + 1155094 q^{97} - 413613 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(228))\)

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
228.6.a \(\chi_{228}(1, \cdot)\) 228.6.a.a 3 1
228.6.a.b 4
228.6.a.c 4
228.6.a.d 5
228.6.c \(\chi_{228}(191, \cdot)\) n/a 180 1
228.6.d \(\chi_{228}(113, \cdot)\) 228.6.d.a 2 1
228.6.d.b 32
228.6.f \(\chi_{228}(151, \cdot)\) 228.6.f.a 50 1
228.6.f.b 50
228.6.i \(\chi_{228}(49, \cdot)\) 228.6.i.a 16 2
228.6.i.b 16
228.6.k \(\chi_{228}(31, \cdot)\) n/a 200 2
228.6.m \(\chi_{228}(11, \cdot)\) n/a 392 2
228.6.p \(\chi_{228}(65, \cdot)\) 228.6.p.a 2 2
228.6.p.b 2
228.6.p.c 64
228.6.q \(\chi_{228}(25, \cdot)\) n/a 102 6
228.6.t \(\chi_{228}(29, \cdot)\) n/a 198 6
228.6.v \(\chi_{228}(23, \cdot)\) n/a 1176 6
228.6.w \(\chi_{228}(67, \cdot)\) n/a 600 6

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(228))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(228)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)