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Properties

Label 124.6
Level 124
Weight 6
Dimension 1368
Nonzero newspaces 8
Sturm bound 5760
Trace bound 1

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Defining parameters

Level: \( N \) = \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(5760\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(124))\).

Total New Old
Modular forms 2475 1428 1047
Cusp forms 2325 1368 957
Eisenstein series 150 60 90

Trace form

\( 1368 q - 15 q^{2} + 24 q^{3} - 15 q^{4} - 138 q^{5} - 15 q^{6} + 176 q^{7} - 15 q^{8} + 168 q^{9} + O(q^{10}) \) \( 1368 q - 15 q^{2} + 24 q^{3} - 15 q^{4} - 138 q^{5} - 15 q^{6} + 176 q^{7} - 15 q^{8} + 168 q^{9} - 15 q^{10} - 1080 q^{11} - 15 q^{12} + 806 q^{13} - 15 q^{14} + 1296 q^{15} - 15 q^{16} - 1218 q^{17} - 15 q^{18} - 1672 q^{19} - 15 q^{20} - 11637 q^{21} - 15 q^{22} + 14973 q^{23} - 15 q^{24} + 22263 q^{25} - 15 q^{26} - 11853 q^{27} - 15 q^{28} - 21492 q^{29} - 30326 q^{31} - 30 q^{32} + 4560 q^{33} - 15 q^{34} + 32754 q^{35} - 15 q^{36} + 75671 q^{37} - 15 q^{38} + 38793 q^{39} - 15 q^{40} - 56067 q^{41} - 15 q^{42} - 18845 q^{43} - 15 q^{44} + 10662 q^{45} - 15 q^{46} + 2592 q^{47} + 293790 q^{48} + 77166 q^{49} - 75690 q^{50} - 228654 q^{51} - 252840 q^{52} - 137148 q^{53} - 432480 q^{54} - 155460 q^{55} - 59280 q^{56} + 89244 q^{57} + 197280 q^{58} + 99006 q^{59} + 769710 q^{60} + 404366 q^{61} + 329295 q^{62} + 370056 q^{63} + 220395 q^{64} + 167604 q^{65} + 6960 q^{66} - 87154 q^{67} - 311970 q^{68} - 493716 q^{69} - 749130 q^{70} - 281796 q^{71} - 1041330 q^{72} - 299284 q^{73} - 261090 q^{74} - 372141 q^{75} + 382560 q^{76} + 258825 q^{77} + 989040 q^{78} + 337609 q^{79} - 15 q^{80} + 542412 q^{81} - 15 q^{82} + 570063 q^{83} - 15 q^{84} + 107958 q^{85} - 15 q^{86} - 114396 q^{87} - 15 q^{88} - 479463 q^{89} - 3660 q^{90} - 594153 q^{91} - 953478 q^{93} - 30 q^{94} - 875208 q^{95} + 3630 q^{96} + 65431 q^{97} - 15 q^{98} + 283245 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(124))\)

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
124.6.a \(\chi_{124}(1, \cdot)\) 124.6.a.a 6 1
124.6.a.b 6
124.6.d \(\chi_{124}(123, \cdot)\) 124.6.d.a 6 1
124.6.d.b 72
124.6.e \(\chi_{124}(5, \cdot)\) 124.6.e.a 26 2
124.6.f \(\chi_{124}(33, \cdot)\) 124.6.f.a 56 4
124.6.g \(\chi_{124}(99, \cdot)\) n/a 156 2
124.6.j \(\chi_{124}(15, \cdot)\) n/a 312 4
124.6.m \(\chi_{124}(9, \cdot)\) n/a 104 8
124.6.p \(\chi_{124}(3, \cdot)\) n/a 624 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(124))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(124)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 2}\)