Properties

Label 177.2.d
Level $177$
Weight $2$
Character orbit 177.d
Rep. character $\chi_{177}(176,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $3$
Sturm bound $40$
Trace bound $2$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(177, [\chi])\).

Total New Old
Modular forms 22 22 0
Cusp forms 18 18 0
Eisenstein series 4 4 0

Trace form

\( 18q - 2q^{3} + 12q^{4} - 10q^{9} + O(q^{10}) \) \( 18q - 2q^{3} + 12q^{4} - 10q^{9} - 14q^{12} + 9q^{15} + 8q^{16} + 8q^{19} - 5q^{21} + 4q^{22} - 38q^{25} + 25q^{27} - 32q^{28} - 42q^{36} + q^{45} - 12q^{46} - 2q^{48} - 10q^{49} + 28q^{51} + 33q^{57} + 40q^{60} + 34q^{63} - 68q^{64} - 52q^{66} + 28q^{75} + 92q^{76} - 16q^{78} - 28q^{79} - 42q^{81} + 40q^{84} + 28q^{85} + 7q^{87} - 80q^{88} + 104q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
177.2.d.a \(6\) \(1.413\) 6.0.19298288.1 None \(-4\) \(-1\) \(0\) \(0\) \(q+(-1+\beta _{1}+\beta _{2}+\beta _{5})q^{2}-\beta _{1}q^{3}+\cdots\)
177.2.d.b \(6\) \(1.413\) 6.0.149721291.1 \(\Q(\sqrt{-59}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-2q^{4}+(\beta _{2}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
177.2.d.c \(6\) \(1.413\) 6.0.19298288.1 None \(4\) \(-1\) \(0\) \(0\) \(q+(1-\beta _{1}-\beta _{2}-\beta _{5})q^{2}-\beta _{1}q^{3}+(2+\cdots)q^{4}+\cdots\)