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Properties

Label 608.6
Level 608
Weight 6
Dimension 32050
Nonzero newspaces 18
Sturm bound 138240
Trace bound 9

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Defining parameters

Level: \( N \) = \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(138240\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(608))\).

Total New Old
Modular forms 58176 32390 25786
Cusp forms 57024 32050 24974
Eisenstein series 1152 340 812

Trace form

\( 32050 q - 64 q^{2} - 46 q^{3} - 64 q^{4} - 140 q^{5} - 64 q^{6} + 146 q^{7} - 64 q^{8} - 670 q^{9} + O(q^{10}) \) \( 32050 q - 64 q^{2} - 46 q^{3} - 64 q^{4} - 140 q^{5} - 64 q^{6} + 146 q^{7} - 64 q^{8} - 670 q^{9} + 336 q^{10} - 46 q^{11} + 3104 q^{12} - 284 q^{13} - 5024 q^{14} - 886 q^{15} - 8424 q^{16} - 3656 q^{17} + 3176 q^{18} - 50 q^{19} + 15064 q^{20} + 11712 q^{21} + 24696 q^{22} + 1282 q^{23} - 42984 q^{24} + 5342 q^{25} - 26024 q^{26} + 14882 q^{27} + 4296 q^{28} - 7420 q^{29} + 64560 q^{30} - 72022 q^{31} + 37096 q^{32} - 21828 q^{33} + 12440 q^{34} + 9506 q^{35} - 131240 q^{36} + 14452 q^{37} - 476 q^{38} + 159916 q^{39} + 57832 q^{40} + 70568 q^{41} + 107176 q^{42} - 64190 q^{43} - 7504 q^{44} - 128436 q^{45} - 126720 q^{46} - 109494 q^{47} - 224808 q^{48} - 135270 q^{49} + 8976 q^{50} + 39770 q^{51} - 37008 q^{52} + 251828 q^{53} - 2696 q^{54} - 49198 q^{55} + 161896 q^{56} + 134920 q^{57} + 169008 q^{58} + 57874 q^{59} + 92104 q^{60} - 409404 q^{61} - 127032 q^{62} + 10602 q^{63} + 98312 q^{64} - 188076 q^{65} + 289952 q^{66} + 122274 q^{67} + 302360 q^{68} + 542336 q^{69} + 112520 q^{70} + 125650 q^{71} - 54256 q^{72} + 160584 q^{73} - 426272 q^{74} - 411560 q^{75} - 256068 q^{76} - 361000 q^{77} - 167088 q^{78} - 495798 q^{79} + 194120 q^{80} - 599462 q^{81} - 870464 q^{82} + 658434 q^{83} - 1195016 q^{84} + 237184 q^{85} - 539848 q^{86} + 1180066 q^{87} + 399608 q^{88} + 518568 q^{89} + 1413608 q^{90} - 400270 q^{91} + 1300584 q^{92} - 303272 q^{93} + 523112 q^{94} - 837390 q^{95} + 1002608 q^{96} - 520296 q^{97} + 791176 q^{98} - 677142 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(608))\)

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
608.6.a \(\chi_{608}(1, \cdot)\) 608.6.a.a 10 1
608.6.a.b 10
608.6.a.c 11
608.6.a.d 11
608.6.a.e 11
608.6.a.f 11
608.6.a.g 13
608.6.a.h 13
608.6.b \(\chi_{608}(303, \cdot)\) 608.6.b.a 2 1
608.6.b.b 96
608.6.c \(\chi_{608}(305, \cdot)\) 608.6.c.a 90 1
608.6.h \(\chi_{608}(607, \cdot)\) 608.6.h.a 100 1
608.6.i \(\chi_{608}(353, \cdot)\) n/a 200 2
608.6.k \(\chi_{608}(153, \cdot)\) None 0 2
608.6.m \(\chi_{608}(151, \cdot)\) None 0 2
608.6.n \(\chi_{608}(31, \cdot)\) n/a 200 2
608.6.s \(\chi_{608}(335, \cdot)\) n/a 196 2
608.6.t \(\chi_{608}(49, \cdot)\) n/a 196 2
608.6.u \(\chi_{608}(75, \cdot)\) n/a 1592 4
608.6.v \(\chi_{608}(77, \cdot)\) n/a 1440 4
608.6.y \(\chi_{608}(161, \cdot)\) n/a 600 6
608.6.z \(\chi_{608}(121, \cdot)\) None 0 4
608.6.bb \(\chi_{608}(103, \cdot)\) None 0 4
608.6.bf \(\chi_{608}(17, \cdot)\) n/a 588 6
608.6.bh \(\chi_{608}(15, \cdot)\) n/a 588 6
608.6.bi \(\chi_{608}(127, \cdot)\) n/a 600 6
608.6.bm \(\chi_{608}(45, \cdot)\) n/a 3184 8
608.6.bn \(\chi_{608}(27, \cdot)\) n/a 3184 8
608.6.bo \(\chi_{608}(71, \cdot)\) None 0 12
608.6.bq \(\chi_{608}(9, \cdot)\) None 0 12
608.6.bs \(\chi_{608}(5, \cdot)\) n/a 9552 24
608.6.bt \(\chi_{608}(3, \cdot)\) n/a 9552 24

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(608))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(608)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 1}\)