Properties

Label 180.2.w
Level $180$
Weight $2$
Character orbit 180.w
Rep. character $\chi_{180}(77,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $24$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 180.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(180, [\chi])\).

Total New Old
Modular forms 168 24 144
Cusp forms 120 24 96
Eisenstein series 48 0 48

Trace form

\( 24q - 2q^{3} + O(q^{10}) \) \( 24q - 2q^{3} + 12q^{11} + 10q^{15} + 4q^{21} - 24q^{23} + 6q^{25} - 26q^{27} - 26q^{33} + 12q^{37} - 36q^{41} - 10q^{45} - 42q^{47} - 76q^{51} + 12q^{55} - 14q^{57} - 12q^{61} + 34q^{63} - 24q^{65} + 6q^{67} + 26q^{75} + 96q^{77} + 56q^{81} + 60q^{83} - 24q^{85} + 88q^{87} - 24q^{91} + 52q^{93} + 60q^{95} - 18q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(180, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
180.2.w.a \(24\) \(1.437\) None \(0\) \(-2\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)