↑

Properties

Label 177.12.d
Level $177$
Weight $12$
Character orbit 177.d
Rep. character $\chi_{177}(176,\cdot)$
Character field $\Q$
Dimension $218$
Sturm bound $240$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(177, [\chi])\).

Total New Old
Modular forms 222 222 0
Cusp forms 218 218 0
Eisenstein series 4 4 0

Trace form

\( 218 q + 1030 q^{3} + 221180 q^{4} + 31504 q^{7} - 344770 q^{9} + O(q^{10}) \) \( 218 q + 1030 q^{3} + 221180 q^{4} + 31504 q^{7} - 344770 q^{9} + 5105284 q^{12} + 9322977 q^{15} + 217834308 q^{16} + 25275368 q^{19} + 5361841 q^{21} + 61406228 q^{22} - 2069374654 q^{25} + 174802813 q^{27} + 219801516 q^{28} + 1448832 q^{36} + 728583499 q^{45} - 2361435732 q^{46} + 4416299224 q^{48} + 55330717222 q^{49} - 4025906948 q^{51} - 8183616969 q^{57} + 51205840696 q^{60} + 7510303906 q^{63} + 195867252160 q^{64} + 7880104004 q^{66} - 146980070132 q^{75} + 145806138848 q^{76} + 11189945384 q^{78} + 72628658132 q^{79} - 17095483554 q^{81} - 306377508740 q^{84} - 44963410988 q^{85} - 231025699241 q^{87} + 88082887712 q^{88} + 325240398808 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

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