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Properties

Label 176.11
Level 176
Weight 11
Dimension 5269
Nonzero newspaces 8
Sturm bound 21120
Trace bound 2

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Defining parameters

Level: \( N \) = \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(21120\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(176))\).

Total New Old
Modular forms 9740 5351 4389
Cusp forms 9460 5269 4191
Eisenstein series 280 82 198

Trace form

\( 5269 q - 16 q^{2} - 11 q^{3} + 2492 q^{4} - 9369 q^{5} + 34412 q^{6} - 7 q^{7} - 138268 q^{8} + 260449 q^{9} + O(q^{10}) \) \( 5269 q - 16 q^{2} - 11 q^{3} + 2492 q^{4} - 9369 q^{5} + 34412 q^{6} - 7 q^{7} - 138268 q^{8} + 260449 q^{9} + 294708 q^{10} + 45891 q^{11} + 21936 q^{12} + 715847 q^{13} - 1515692 q^{14} - 15 q^{15} + 938044 q^{16} + 4406279 q^{17} - 4133872 q^{18} + 10214069 q^{19} - 10603052 q^{20} + 10846868 q^{21} + 20568904 q^{22} + 16559466 q^{23} - 117039476 q^{24} - 60543667 q^{25} + 36903004 q^{26} + 51743089 q^{27} + 72919548 q^{28} + 61670567 q^{29} - 265562524 q^{30} - 15 q^{31} + 105323484 q^{32} - 284457537 q^{33} - 136949840 q^{34} + 299360105 q^{35} + 31621332 q^{36} + 262666975 q^{37} - 312092020 q^{38} + 451588649 q^{39} + 250763420 q^{40} - 27193257 q^{41} - 214790852 q^{42} - 344973744 q^{43} - 73664008 q^{44} + 722741326 q^{45} + 875241652 q^{46} - 189128295 q^{47} - 1250380772 q^{48} - 2708465835 q^{49} + 1751520608 q^{50} + 1306103385 q^{51} + 1542784868 q^{52} - 453672417 q^{53} - 1827300948 q^{54} + 1428448493 q^{55} + 2771246888 q^{56} - 4257413757 q^{57} - 75123460 q^{58} - 3087367723 q^{59} - 637739220 q^{60} + 3211916615 q^{61} + 1966125964 q^{62} - 295260 q^{63} + 1735357292 q^{64} - 10935104104 q^{65} - 768197880 q^{66} + 9660855462 q^{67} + 1711655564 q^{68} + 10827196674 q^{69} + 4558259992 q^{70} - 14788846887 q^{71} + 34397115560 q^{72} - 4533193241 q^{73} - 34844519408 q^{74} + 8416834541 q^{75} - 26534452028 q^{76} + 12991986011 q^{77} + 44978880464 q^{78} + 19364580385 q^{79} + 93677001496 q^{80} + 25740345005 q^{81} - 34218616316 q^{82} - 50023375091 q^{83} - 107445031732 q^{84} - 60551302841 q^{85} - 33698283260 q^{86} + 63665225312 q^{87} + 90618193588 q^{88} + 46629937314 q^{89} + 163765219260 q^{90} - 5348181463 q^{91} - 1053890340 q^{92} - 34221833241 q^{93} - 72461015588 q^{94} - 38537879615 q^{95} - 234088654444 q^{96} - 65417954249 q^{97} - 6150278180 q^{98} + 36910489483 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(176))\)

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
176.11.b \(\chi_{176}(153, \cdot)\) None 0 1
176.11.d \(\chi_{176}(111, \cdot)\) 176.11.d.a 18 1
176.11.d.b 32
176.11.f \(\chi_{176}(23, \cdot)\) None 0 1
176.11.h \(\chi_{176}(65, \cdot)\) 176.11.h.a 1 1
176.11.h.b 2
176.11.h.c 8
176.11.h.d 8
176.11.h.e 10
176.11.h.f 30
176.11.k \(\chi_{176}(67, \cdot)\) n/a 400 2
176.11.l \(\chi_{176}(21, \cdot)\) n/a 476 2
176.11.n \(\chi_{176}(17, \cdot)\) n/a 236 4
176.11.p \(\chi_{176}(71, \cdot)\) None 0 4
176.11.r \(\chi_{176}(15, \cdot)\) n/a 240 4
176.11.t \(\chi_{176}(41, \cdot)\) None 0 4
176.11.u \(\chi_{176}(13, \cdot)\) n/a 1904 8
176.11.v \(\chi_{176}(3, \cdot)\) n/a 1904 8

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

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(176))\) into lower level spaces

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