Properties

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

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Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 180.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(180))\).

Total New Old
Modular forms 48 1 47
Cusp forms 25 1 24
Eisenstein series 23 0 23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)FrickeDim.
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q + q^{5} + 2q^{7} + O(q^{10}) \) \( q + q^{5} + 2q^{7} + 2q^{13} + 6q^{17} - 4q^{19} - 6q^{23} + q^{25} - 6q^{29} - 4q^{31} + 2q^{35} + 2q^{37} - 6q^{41} - 10q^{43} + 6q^{47} - 3q^{49} + 6q^{53} - 12q^{59} + 2q^{61} + 2q^{65} + 2q^{67} + 12q^{71} + 2q^{73} + 8q^{79} - 6q^{83} + 6q^{85} + 6q^{89} + 4q^{91} - 4q^{95} + 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(180))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5
180.2.a.a \(1\) \(1.437\) \(\Q\) None \(0\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(q+q^{5}+2q^{7}+2q^{13}+6q^{17}-4q^{19}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(180))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(180)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)