Properties

Label 180.2.d
Level $180$
Weight $2$
Character orbit 180.d
Rep. character $\chi_{180}(109,\cdot)$
Character field $\Q$
Dimension $2$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
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 48 2 46
Cusp forms 24 2 22
Eisenstein series 24 0 24

Trace form

\( 2q - 2q^{5} + O(q^{10}) \) \( 2q - 2q^{5} + 8q^{11} - 6q^{25} - 12q^{29} + 8q^{31} - 16q^{35} + 20q^{41} - 18q^{49} - 8q^{55} + 8q^{59} + 4q^{61} + 24q^{79} + 16q^{85} - 20q^{89} + O(q^{100}) \)

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.d.a \(2\) \(1.437\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+i)q^{5}+2iq^{7}+4q^{11}-2iq^{17}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)