Properties

Label 180.2.i
Level $180$
Weight $2$
Character orbit 180.i
Rep. character $\chi_{180}(61,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 180.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 84 8 76
Cusp forms 60 8 52
Eisenstein series 24 0 24

Trace form

\( 8q + 2q^{3} + 2q^{5} - 2q^{7} + 8q^{9} + O(q^{10}) \) \( 8q + 2q^{3} + 2q^{5} - 2q^{7} + 8q^{9} - 2q^{13} - 2q^{15} - 12q^{17} + 16q^{19} - 20q^{21} + 6q^{23} - 4q^{25} + 2q^{27} + 4q^{31} + 12q^{33} - 8q^{35} + 4q^{37} - 8q^{39} - 12q^{41} - 2q^{43} - 8q^{45} - 24q^{47} - 12q^{49} + 12q^{51} - 24q^{53} - 26q^{57} - 20q^{61} - 32q^{63} + 10q^{65} - 20q^{67} + 24q^{69} + 72q^{71} + 40q^{73} + 2q^{75} - 6q^{77} + 4q^{79} + 20q^{81} + 30q^{83} + 6q^{85} + 42q^{87} + 8q^{91} + 46q^{93} + 4q^{95} - 8q^{97} + 12q^{99} + O(q^{100}) \)

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.i.a \(2\) \(1.437\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-1\) \(1\) \(q+(2-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
180.2.i.b \(6\) \(1.437\) 6.0.954288.1 None \(0\) \(-1\) \(3\) \(-3\) \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)