Properties

Label 175.6
Level 175
Weight 6
Dimension 5197
Nonzero newspaces 12
Sturm bound 14400
Trace bound 2

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Defining parameters

Level: \( N \) = \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(14400\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(175))\).

Total New Old
Modular forms 6168 5401 767
Cusp forms 5832 5197 635
Eisenstein series 336 204 132

Trace form

\( 5197 q - 11 q^{2} - 44 q^{3} - 163 q^{4} - 158 q^{5} + 778 q^{6} + 239 q^{7} - 709 q^{8} - 1257 q^{9} + O(q^{10}) \) \( 5197 q - 11 q^{2} - 44 q^{3} - 163 q^{4} - 158 q^{5} + 778 q^{6} + 239 q^{7} - 709 q^{8} - 1257 q^{9} - 808 q^{10} + 1604 q^{11} - 1878 q^{12} - 1210 q^{13} + 583 q^{14} + 2364 q^{15} + 4281 q^{16} - 484 q^{17} - 14237 q^{18} - 18100 q^{19} - 20548 q^{20} - 8364 q^{21} + 17824 q^{22} + 34252 q^{23} + 118534 q^{24} + 51314 q^{25} + 15468 q^{26} - 44612 q^{27} - 120181 q^{28} - 135514 q^{29} - 128156 q^{30} - 4972 q^{31} + 42623 q^{32} + 126678 q^{33} + 219966 q^{34} + 80688 q^{35} + 292821 q^{36} + 79138 q^{37} + 99652 q^{38} - 151560 q^{39} - 282056 q^{40} - 233370 q^{41} - 541408 q^{42} - 240320 q^{43} - 253424 q^{44} + 47438 q^{45} + 164702 q^{46} + 295076 q^{47} + 782322 q^{48} + 162797 q^{49} + 504804 q^{50} + 189648 q^{51} + 265072 q^{52} + 150946 q^{53} + 53294 q^{54} + 36116 q^{55} + 108737 q^{56} - 678064 q^{57} - 1134378 q^{58} - 715160 q^{59} - 725308 q^{60} - 495500 q^{61} - 813668 q^{62} - 357107 q^{63} - 313111 q^{64} - 174386 q^{65} + 778670 q^{66} + 651812 q^{67} + 876522 q^{68} + 1164976 q^{69} + 961982 q^{70} + 990660 q^{71} + 2582355 q^{72} + 789360 q^{73} + 695596 q^{74} + 508348 q^{75} - 104814 q^{76} - 354300 q^{77} - 1339768 q^{78} - 1000908 q^{79} - 855632 q^{80} - 1420971 q^{81} - 786770 q^{82} - 626872 q^{83} - 408824 q^{84} - 1003338 q^{85} + 618296 q^{86} + 51644 q^{87} - 1613600 q^{88} - 1267326 q^{89} - 2030340 q^{90} - 835208 q^{91} - 1726180 q^{92} - 1002362 q^{93} - 595566 q^{94} + 128028 q^{95} - 720334 q^{96} + 1864790 q^{97} + 1504127 q^{98} + 2592804 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(175))\)

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
175.6.a \(\chi_{175}(1, \cdot)\) 175.6.a.a 1 1
175.6.a.b 1
175.6.a.c 2
175.6.a.d 2
175.6.a.e 3
175.6.a.f 4
175.6.a.g 4
175.6.a.h 4
175.6.a.i 6
175.6.a.j 6
175.6.a.k 7
175.6.a.l 7
175.6.b \(\chi_{175}(99, \cdot)\) 175.6.b.a 2 1
175.6.b.b 2
175.6.b.c 4
175.6.b.d 4
175.6.b.e 6
175.6.b.f 8
175.6.b.g 8
175.6.b.h 12
175.6.e \(\chi_{175}(51, \cdot)\) n/a 120 2
175.6.f \(\chi_{175}(118, \cdot)\) n/a 116 2
175.6.h \(\chi_{175}(36, \cdot)\) n/a 304 4
175.6.k \(\chi_{175}(74, \cdot)\) n/a 116 2
175.6.n \(\chi_{175}(29, \cdot)\) n/a 296 4
175.6.o \(\chi_{175}(68, \cdot)\) n/a 232 4
175.6.q \(\chi_{175}(11, \cdot)\) n/a 784 8
175.6.s \(\chi_{175}(13, \cdot)\) n/a 784 8
175.6.t \(\chi_{175}(4, \cdot)\) n/a 784 8
175.6.x \(\chi_{175}(3, \cdot)\) n/a 1568 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(175))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(175)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 1}\)