Properties

Label 152.6
Level 152
Weight 6
Dimension 1979
Nonzero newspaces 9
Sturm bound 8640
Trace bound 3

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Defining parameters

Level: \( N \) = \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 9 \)
Sturm bound: \(8640\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(152))\).

Total New Old
Modular forms 3708 2047 1661
Cusp forms 3492 1979 1513
Eisenstein series 216 68 148

Trace form

\( 1979 q - 14 q^{2} - 58 q^{3} - 58 q^{4} + 148 q^{5} + 214 q^{6} - 162 q^{7} + 478 q^{8} - 22 q^{9} + O(q^{10}) \) \( 1979 q - 14 q^{2} - 58 q^{3} - 58 q^{4} + 148 q^{5} + 214 q^{6} - 162 q^{7} + 478 q^{8} - 22 q^{9} - 1282 q^{10} - 266 q^{11} - 3170 q^{12} - 956 q^{13} + 4750 q^{14} + 3774 q^{15} + 6606 q^{16} + 1960 q^{17} - 9526 q^{18} - 3062 q^{19} - 9284 q^{20} + 960 q^{21} + 11254 q^{22} - 5058 q^{23} + 15566 q^{24} - 7850 q^{25} - 11234 q^{26} - 20239 q^{27} - 10322 q^{28} + 17922 q^{29} + 4238 q^{30} + 56932 q^{31} - 10834 q^{32} + 12614 q^{33} + 9526 q^{34} - 33126 q^{35} + 20310 q^{36} - 45294 q^{37} - 15998 q^{38} - 147090 q^{39} - 32082 q^{40} + 27430 q^{41} + 52270 q^{42} + 72322 q^{43} + 58206 q^{44} + 159262 q^{45} - 58418 q^{46} + 96132 q^{47} - 71250 q^{48} - 22672 q^{49} + 94978 q^{50} - 51359 q^{51} + 73102 q^{52} - 23372 q^{53} - 42220 q^{54} - 152610 q^{55} - 81554 q^{56} - 58884 q^{57} - 7604 q^{58} - 33770 q^{59} + 488898 q^{60} + 149806 q^{61} + 18380 q^{62} + 133606 q^{63} - 563458 q^{64} - 175102 q^{65} - 823890 q^{66} - 431086 q^{67} - 395052 q^{68} - 7360 q^{69} + 197238 q^{70} - 247468 q^{71} + 1063196 q^{72} + 291773 q^{73} + 721774 q^{74} + 614710 q^{75} + 898858 q^{76} + 277086 q^{77} + 1078730 q^{78} + 747436 q^{79} + 218622 q^{80} + 13527 q^{81} - 1113112 q^{82} - 402100 q^{83} - 1861082 q^{84} - 177304 q^{85} - 1119824 q^{86} - 1486614 q^{87} - 862370 q^{88} - 298490 q^{89} - 576178 q^{90} + 305814 q^{91} + 1197984 q^{92} + 647242 q^{93} + 1542330 q^{94} - 294814 q^{95} + 231260 q^{96} + 85220 q^{97} + 234066 q^{98} + 590731 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(152))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
152.6.a \(\chi_{152}(1, \cdot)\) 152.6.a.a 1 1
152.6.a.b 3
152.6.a.c 6
152.6.a.d 6
152.6.a.e 7
152.6.b \(\chi_{152}(75, \cdot)\) 152.6.b.a 2 1
152.6.b.b 96
152.6.c \(\chi_{152}(77, \cdot)\) 152.6.c.a 90 1
152.6.h \(\chi_{152}(151, \cdot)\) None 0 1
152.6.i \(\chi_{152}(49, \cdot)\) 152.6.i.a 24 2
152.6.i.b 26
152.6.j \(\chi_{152}(31, \cdot)\) None 0 2
152.6.o \(\chi_{152}(27, \cdot)\) n/a 196 2
152.6.p \(\chi_{152}(45, \cdot)\) n/a 196 2
152.6.q \(\chi_{152}(9, \cdot)\) n/a 150 6
152.6.t \(\chi_{152}(5, \cdot)\) n/a 588 6
152.6.v \(\chi_{152}(3, \cdot)\) n/a 588 6
152.6.w \(\chi_{152}(15, \cdot)\) None 0 6

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(152))\) into lower level spaces

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