Properties

Label 608.4
Level 608
Weight 4
Dimension 19162
Nonzero newspaces 18
Sturm bound 92160
Trace bound 9

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Defining parameters

Level: \( N \) = \( 608 = 2^{5} \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(92160\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(608))\).

Total New Old
Modular forms 35136 19502 15634
Cusp forms 33984 19162 14822
Eisenstein series 1152 340 812

Trace form

\( 19162 q - 64 q^{2} - 46 q^{3} - 64 q^{4} - 68 q^{5} - 64 q^{6} - 78 q^{7} - 64 q^{8} - 190 q^{9} + O(q^{10}) \) \( 19162 q - 64 q^{2} - 46 q^{3} - 64 q^{4} - 68 q^{5} - 64 q^{6} - 78 q^{7} - 64 q^{8} - 190 q^{9} - 304 q^{10} - 46 q^{11} + 32 q^{12} + 172 q^{13} + 352 q^{14} + 170 q^{15} + 536 q^{16} + 328 q^{17} + 296 q^{18} - 50 q^{19} - 296 q^{20} - 576 q^{21} - 456 q^{22} - 1310 q^{23} + 24 q^{24} - 770 q^{25} - 104 q^{26} + 482 q^{27} - 824 q^{28} + 332 q^{29} - 2448 q^{30} + 2346 q^{31} - 1304 q^{32} + 780 q^{33} - 1128 q^{34} + 866 q^{35} - 2984 q^{36} - 1732 q^{37} - 1052 q^{38} - 2420 q^{39} + 1000 q^{40} - 1000 q^{41} + 4456 q^{42} - 1662 q^{43} + 4016 q^{44} + 2388 q^{45} + 2816 q^{46} + 1290 q^{47} + 4824 q^{48} + 2114 q^{49} + 7056 q^{50} + 2714 q^{51} + 4976 q^{52} - 964 q^{53} + 2104 q^{54} - 142 q^{55} - 2456 q^{56} - 1136 q^{57} - 6544 q^{58} - 2798 q^{59} - 11576 q^{60} + 1804 q^{61} - 6840 q^{62} - 5046 q^{63} - 9976 q^{64} - 3612 q^{65} - 12064 q^{66} - 4126 q^{67} - 5608 q^{68} + 512 q^{69} - 2872 q^{70} - 782 q^{71} + 3344 q^{72} + 1400 q^{73} + 6880 q^{74} + 3352 q^{75} + 5052 q^{76} - 1384 q^{77} + 23760 q^{78} - 1910 q^{79} + 20552 q^{80} + 2962 q^{81} + 12736 q^{82} - 4926 q^{83} + 13048 q^{84} + 1872 q^{85} + 1784 q^{86} + 5890 q^{87} - 2568 q^{88} + 3480 q^{89} - 14872 q^{90} + 7154 q^{91} - 20376 q^{92} - 10088 q^{93} - 25752 q^{94} + 5250 q^{95} - 35728 q^{96} - 4888 q^{97} - 22520 q^{98} + 10794 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(608))\)

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
608.4.a \(\chi_{608}(1, \cdot)\) 608.4.a.a 1 1
608.4.a.b 1
608.4.a.c 2
608.4.a.d 2
608.4.a.e 5
608.4.a.f 5
608.4.a.g 5
608.4.a.h 5
608.4.a.i 7
608.4.a.j 7
608.4.a.k 7
608.4.a.l 7
608.4.b \(\chi_{608}(303, \cdot)\) 608.4.b.a 2 1
608.4.b.b 56
608.4.c \(\chi_{608}(305, \cdot)\) 608.4.c.a 54 1
608.4.h \(\chi_{608}(607, \cdot)\) 608.4.h.a 60 1
608.4.i \(\chi_{608}(353, \cdot)\) n/a 120 2
608.4.k \(\chi_{608}(153, \cdot)\) None 0 2
608.4.m \(\chi_{608}(151, \cdot)\) None 0 2
608.4.n \(\chi_{608}(31, \cdot)\) n/a 120 2
608.4.s \(\chi_{608}(335, \cdot)\) n/a 116 2
608.4.t \(\chi_{608}(49, \cdot)\) n/a 116 2
608.4.u \(\chi_{608}(75, \cdot)\) n/a 952 4
608.4.v \(\chi_{608}(77, \cdot)\) n/a 864 4
608.4.y \(\chi_{608}(161, \cdot)\) n/a 360 6
608.4.z \(\chi_{608}(121, \cdot)\) None 0 4
608.4.bb \(\chi_{608}(103, \cdot)\) None 0 4
608.4.bf \(\chi_{608}(17, \cdot)\) n/a 348 6
608.4.bh \(\chi_{608}(15, \cdot)\) n/a 348 6
608.4.bi \(\chi_{608}(127, \cdot)\) n/a 360 6
608.4.bm \(\chi_{608}(45, \cdot)\) n/a 1904 8
608.4.bn \(\chi_{608}(27, \cdot)\) n/a 1904 8
608.4.bo \(\chi_{608}(71, \cdot)\) None 0 12
608.4.bq \(\chi_{608}(9, \cdot)\) None 0 12
608.4.bs \(\chi_{608}(5, \cdot)\) n/a 5712 24
608.4.bt \(\chi_{608}(3, \cdot)\) n/a 5712 24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(608))\) into lower level spaces

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