Properties

Label 45.2.a
Level $45$
Weight $2$
Character orbit 45.a
Rep. character $\chi_{45}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(45))\).

Total New Old
Modular forms 10 1 9
Cusp forms 3 1 2
Eisenstein series 7 0 7

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

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

Trace form

\( q + q^{2} - q^{4} - q^{5} - 3q^{8} + O(q^{10}) \) \( q + q^{2} - q^{4} - q^{5} - 3q^{8} - q^{10} + 4q^{11} - 2q^{13} - q^{16} - 2q^{17} + 4q^{19} + q^{20} + 4q^{22} + q^{25} - 2q^{26} + 2q^{29} + 5q^{32} - 2q^{34} - 10q^{37} + 4q^{38} + 3q^{40} - 10q^{41} + 4q^{43} - 4q^{44} - 8q^{47} - 7q^{49} + q^{50} + 2q^{52} + 10q^{53} - 4q^{55} + 2q^{58} + 4q^{59} - 2q^{61} + 7q^{64} + 2q^{65} + 12q^{67} + 2q^{68} + 8q^{71} + 10q^{73} - 10q^{74} - 4q^{76} + q^{80} - 10q^{82} - 12q^{83} + 2q^{85} + 4q^{86} - 12q^{88} + 6q^{89} - 8q^{94} - 4q^{95} + 2q^{97} - 7q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(45))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5
45.2.a.a \(1\) \(0.359\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+4q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(45))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(45)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)