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Properties

Label 152.4
Level 152
Weight 4
Dimension 1173
Nonzero newspaces 9
Newform subspaces 17
Sturm bound 5760
Trace bound 3

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Defining parameters

Level: \( N \) = \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 17 \)
Sturm bound: \(5760\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(152))\).

Total New Old
Modular forms 2268 1241 1027
Cusp forms 2052 1173 879
Eisenstein series 216 68 148

Trace form

\( 1173 q - 14 q^{2} - 10 q^{3} + 6 q^{4} + 4 q^{5} - 74 q^{6} - 34 q^{7} - 98 q^{8} - 10 q^{9} + O(q^{10}) \) \( 1173 q - 14 q^{2} - 10 q^{3} + 6 q^{4} + 4 q^{5} - 74 q^{6} - 34 q^{7} - 98 q^{8} - 10 q^{9} + 94 q^{10} + 70 q^{11} + 94 q^{12} - 44 q^{13} - 50 q^{14} - 258 q^{15} - 50 q^{16} - 80 q^{17} - 22 q^{18} - 62 q^{19} - 260 q^{20} + 192 q^{21} + 150 q^{22} + 702 q^{23} + 206 q^{24} + 154 q^{25} - 578 q^{26} - 979 q^{27} - 210 q^{28} - 1026 q^{29} + 206 q^{30} - 684 q^{31} + 686 q^{32} + 194 q^{33} - 74 q^{34} + 1194 q^{35} - 42 q^{36} + 990 q^{37} + 178 q^{38} + 3150 q^{39} - 466 q^{40} + 1090 q^{41} + 430 q^{42} + 130 q^{43} - 354 q^{44} - 1070 q^{45} - 626 q^{46} - 3372 q^{47} - 1362 q^{48} - 1096 q^{49} + 34 q^{50} - 923 q^{51} + 1102 q^{52} + 484 q^{53} - 988 q^{54} + 478 q^{55} + 622 q^{56} - 252 q^{57} + 1644 q^{58} + 1318 q^{59} + 7266 q^{60} + 1330 q^{61} + 10508 q^{62} + 6310 q^{63} + 7038 q^{64} - 298 q^{65} + 2478 q^{66} - 718 q^{67} - 2748 q^{68} - 448 q^{69} - 10634 q^{70} - 4156 q^{71} - 16948 q^{72} - 4757 q^{73} - 13106 q^{74} - 10418 q^{75} - 13910 q^{76} - 1830 q^{77} - 13558 q^{78} - 4788 q^{79} - 5250 q^{80} - 39 q^{81} - 9208 q^{82} - 1516 q^{83} - 1562 q^{84} + 200 q^{85} + 9040 q^{86} + 4362 q^{87} + 10974 q^{88} + 3250 q^{89} + 19310 q^{90} + 10806 q^{91} + 14064 q^{92} + 2878 q^{93} + 10938 q^{94} - 7390 q^{95} + 860 q^{96} - 8780 q^{97} - 1134 q^{98} - 7097 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(152))\)

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
152.4.a \(\chi_{152}(1, \cdot)\) 152.4.a.a 2 1
152.4.a.b 3
152.4.a.c 3
152.4.a.d 5
152.4.b \(\chi_{152}(75, \cdot)\) 152.4.b.a 2 1
152.4.b.b 56
152.4.c \(\chi_{152}(77, \cdot)\) 152.4.c.a 54 1
152.4.h \(\chi_{152}(151, \cdot)\) None 0 1
152.4.i \(\chi_{152}(49, \cdot)\) 152.4.i.a 14 2
152.4.i.b 16
152.4.j \(\chi_{152}(31, \cdot)\) None 0 2
152.4.o \(\chi_{152}(27, \cdot)\) 152.4.o.a 4 2
152.4.o.b 112
152.4.p \(\chi_{152}(45, \cdot)\) 152.4.p.a 116 2
152.4.q \(\chi_{152}(9, \cdot)\) 152.4.q.a 42 6
152.4.q.b 48
152.4.t \(\chi_{152}(5, \cdot)\) 152.4.t.a 348 6
152.4.v \(\chi_{152}(3, \cdot)\) 152.4.v.a 12 6
152.4.v.b 336
152.4.w \(\chi_{152}(15, \cdot)\) None 0 6

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(152))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(152)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 1}\)