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Properties

Label 177.11.b
Level $177$
Weight $11$
Character orbit 177.b
Rep. character $\chi_{177}(119,\cdot)$
Character field $\Q$
Dimension $194$
Sturm bound $220$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Sturm bound: \(220\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(177, [\chi])\).

Total New Old
Modular forms 202 194 8
Cusp forms 198 194 4
Eisenstein series 4 0 4

Trace form

\( 194 q - 101572 q^{4} + 12160 q^{6} - 50548 q^{7} + 169100 q^{9} + O(q^{10}) \) \( 194 q - 101572 q^{4} + 12160 q^{6} - 50548 q^{7} + 169100 q^{9} + 42276 q^{10} + 678612 q^{13} - 116807 q^{15} + 51702996 q^{16} + 3277030 q^{18} - 1355172 q^{19} - 4599677 q^{21} - 16850412 q^{22} + 24805770 q^{24} - 379567906 q^{25} - 7837539 q^{27} - 10989172 q^{28} + 76749342 q^{30} + 101279688 q^{31} - 65775058 q^{33} - 113129876 q^{34} + 41469600 q^{36} + 197862592 q^{37} + 55879538 q^{39} - 657314056 q^{40} + 76317590 q^{42} - 310701348 q^{43} + 456460225 q^{45} + 643181644 q^{46} - 470081404 q^{48} + 8426551894 q^{49} + 945509212 q^{51} + 820675320 q^{52} - 2583387150 q^{54} + 1292684292 q^{55} + 518271219 q^{57} + 1195633904 q^{58} - 2104441672 q^{60} - 4982511292 q^{61} - 1122587302 q^{63} - 23916589952 q^{64} + 3641344152 q^{66} - 4417918844 q^{67} + 2229626016 q^{69} + 377377508 q^{70} - 6181502978 q^{72} + 7876610768 q^{73} + 3116210862 q^{75} + 5759293872 q^{76} + 13458713956 q^{78} - 14432262464 q^{79} - 17139207348 q^{81} - 8080384596 q^{82} - 776926620 q^{84} + 11897234068 q^{85} - 3810838133 q^{87} - 6632111856 q^{88} + 20968077464 q^{90} - 11964248244 q^{91} - 8417485526 q^{93} - 26473658448 q^{94} + 6093451702 q^{96} - 10950944784 q^{97} + 19475317442 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{11}^{\mathrm{old}}(177, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(177, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)