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Properties

Label 154.6
Level 154
Weight 6
Dimension 1130
Nonzero newspaces 8
Sturm bound 8640
Trace bound 4

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Defining parameters

Level: \( N \) = \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(8640\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(154))\).

Total New Old
Modular forms 3720 1130 2590
Cusp forms 3480 1130 2350
Eisenstein series 240 0 240

Trace form

\( 1130 q - 36 q^{3} + 64 q^{4} - 132 q^{5} - 472 q^{6} + 126 q^{7} + 236 q^{9} + O(q^{10}) \) \( 1130 q - 36 q^{3} + 64 q^{4} - 132 q^{5} - 472 q^{6} + 126 q^{7} + 236 q^{9} - 512 q^{10} - 1336 q^{11} - 896 q^{12} - 5280 q^{13} + 2440 q^{14} + 18116 q^{15} + 1024 q^{16} + 8056 q^{17} - 12616 q^{18} - 11506 q^{19} - 4800 q^{20} - 26400 q^{21} - 2832 q^{22} - 31176 q^{23} + 3200 q^{24} + 38796 q^{25} + 56144 q^{26} + 115734 q^{27} + 16352 q^{28} + 12776 q^{29} - 45936 q^{30} - 105892 q^{31} - 10240 q^{32} - 119834 q^{33} - 58304 q^{34} + 17696 q^{35} - 45280 q^{36} - 23712 q^{37} + 84288 q^{38} + 138140 q^{39} + 63488 q^{40} + 91832 q^{41} + 87928 q^{42} - 48844 q^{43} - 4256 q^{44} - 97984 q^{45} + 12160 q^{46} + 57368 q^{47} - 9216 q^{48} - 68740 q^{49} - 145472 q^{50} - 10610 q^{51} - 39360 q^{52} - 3340 q^{53} - 54144 q^{54} - 39572 q^{55} + 42240 q^{56} + 262086 q^{57} - 10144 q^{58} + 192986 q^{59} - 21888 q^{60} + 491532 q^{61} + 66912 q^{62} - 259900 q^{63} - 81920 q^{64} - 651476 q^{65} - 638240 q^{66} - 790428 q^{67} - 131264 q^{68} - 1018368 q^{69} - 108944 q^{70} + 432480 q^{71} + 111104 q^{72} + 671996 q^{73} + 294880 q^{74} + 1988950 q^{75} + 177600 q^{76} + 1186152 q^{77} + 462208 q^{78} + 739824 q^{79} + 78848 q^{80} - 600570 q^{81} - 88984 q^{82} - 621010 q^{83} - 279616 q^{84} - 301884 q^{85} - 504472 q^{86} - 1377956 q^{87} - 358400 q^{88} - 56032 q^{89} - 387456 q^{90} - 195140 q^{91} + 86592 q^{92} + 943040 q^{93} + 345104 q^{94} + 936608 q^{95} + 61440 q^{96} + 284898 q^{97} + 3992 q^{98} - 1198640 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(154))\)

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
154.6.a \(\chi_{154}(1, \cdot)\) 154.6.a.a 1 1
154.6.a.b 1
154.6.a.c 1
154.6.a.d 2
154.6.a.e 2
154.6.a.f 3
154.6.a.g 3
154.6.a.h 4
154.6.a.i 4
154.6.a.j 5
154.6.c \(\chi_{154}(153, \cdot)\) 154.6.c.a 40 1
154.6.e \(\chi_{154}(23, \cdot)\) 154.6.e.a 16 2
154.6.e.b 16
154.6.e.c 16
154.6.e.d 16
154.6.f \(\chi_{154}(15, \cdot)\) n/a 120 4
154.6.i \(\chi_{154}(87, \cdot)\) 154.6.i.a 80 2
154.6.k \(\chi_{154}(13, \cdot)\) n/a 160 4
154.6.m \(\chi_{154}(9, \cdot)\) n/a 320 8
154.6.n \(\chi_{154}(17, \cdot)\) n/a 320 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(154))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(154)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)