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Properties

Label 176.9
Level 176
Weight 9
Dimension 4207
Nonzero newspaces 8
Sturm bound 17280
Trace bound 2

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Defining parameters

Level: \( N \) = \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(17280\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(176))\).

Total New Old
Modular forms 7820 4289 3531
Cusp forms 7540 4207 3333
Eisenstein series 280 82 198

Trace form

\( 4207 q - 16 q^{2} - 11 q^{3} - 388 q^{4} + 987 q^{5} - 6484 q^{6} - 7 q^{7} + 17444 q^{8} + 28915 q^{9} + O(q^{10}) \) \( 4207 q - 16 q^{2} - 11 q^{3} - 388 q^{4} + 987 q^{5} - 6484 q^{6} - 7 q^{7} + 17444 q^{8} + 28915 q^{9} + 3700 q^{10} + 19763 q^{11} - 28176 q^{12} + 34267 q^{13} + 117780 q^{14} - 15 q^{15} - 490692 q^{16} + 33227 q^{17} + 447440 q^{18} - 335115 q^{19} + 270740 q^{20} - 1242508 q^{21} - 985720 q^{22} + 1691114 q^{23} + 1601164 q^{24} + 1818339 q^{25} + 369500 q^{26} - 77327 q^{27} - 188292 q^{28} - 5720997 q^{29} - 3763420 q^{30} - 15 q^{31} + 6790364 q^{32} - 864777 q^{33} - 3269840 q^{34} + 2622905 q^{35} - 3754668 q^{36} - 12189253 q^{37} + 6020684 q^{38} + 3366329 q^{39} - 6513892 q^{40} + 613675 q^{41} + 7462588 q^{42} - 12629648 q^{43} + 10360920 q^{44} - 1372838 q^{45} - 3021580 q^{46} + 15593745 q^{47} - 9183716 q^{48} - 20391081 q^{49} - 29505440 q^{50} - 10606215 q^{51} - 8671324 q^{52} - 61490757 q^{53} - 37334100 q^{54} + 13575765 q^{55} + 72692776 q^{56} + 48044187 q^{57} + 2069372 q^{58} + 92008309 q^{59} + 41374380 q^{60} + 110599387 q^{61} + 128086924 q^{62} - 32820 q^{63} - 101654932 q^{64} - 46337216 q^{65} - 65035800 q^{66} - 118949146 q^{67} - 148678644 q^{68} + 67903818 q^{69} - 193461032 q^{70} + 106512761 q^{71} + 460690856 q^{72} + 379838059 q^{73} + 623037200 q^{74} - 209335315 q^{75} - 245406204 q^{76} - 367508565 q^{77} - 1070085616 q^{78} - 137089615 q^{79} - 56070568 q^{80} + 15896015 q^{81} + 293736388 q^{82} + 330603349 q^{83} + 365064140 q^{84} + 1074991951 q^{85} + 375641732 q^{86} - 299425312 q^{87} - 673896268 q^{88} - 681814426 q^{89} - 840077508 q^{90} - 285142855 q^{91} - 164161956 q^{92} - 299663385 q^{93} + 93481564 q^{94} + 109569585 q^{95} + 464258324 q^{96} + 828671115 q^{97} + 1205233372 q^{98} + 355788115 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(176))\)

We only show spaces with odd 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
176.9.b \(\chi_{176}(153, \cdot)\) None 0 1
176.9.d \(\chi_{176}(111, \cdot)\) 176.9.d.a 12 1
176.9.d.b 28
176.9.f \(\chi_{176}(23, \cdot)\) None 0 1
176.9.h \(\chi_{176}(65, \cdot)\) 176.9.h.a 1 1
176.9.h.b 2
176.9.h.c 6
176.9.h.d 6
176.9.h.e 8
176.9.h.f 24
176.9.k \(\chi_{176}(67, \cdot)\) n/a 320 2
176.9.l \(\chi_{176}(21, \cdot)\) n/a 380 2
176.9.n \(\chi_{176}(17, \cdot)\) n/a 188 4
176.9.p \(\chi_{176}(71, \cdot)\) None 0 4
176.9.r \(\chi_{176}(15, \cdot)\) n/a 192 4
176.9.t \(\chi_{176}(41, \cdot)\) None 0 4
176.9.u \(\chi_{176}(13, \cdot)\) n/a 1520 8
176.9.v \(\chi_{176}(3, \cdot)\) n/a 1520 8

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(176))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(176)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)