Properties

Label 145.2.a
Level $145$
Weight $2$
Character orbit 145.a
Rep. character $\chi_{145}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $4$
Sturm bound $30$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 145 = 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 145.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(30\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(145))\).

Total New Old
Modular forms 16 9 7
Cusp forms 13 9 4
Eisenstein series 3 0 3

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

\(5\)\(29\)FrickeDim
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(6\)

Trace form

\( 9 q + q^{2} - 4 q^{3} + 7 q^{4} + q^{5} + 4 q^{6} - 4 q^{7} + 9 q^{8} + 5 q^{9} - 3 q^{10} - 16 q^{12} - 10 q^{13} - 8 q^{14} + 7 q^{16} - 6 q^{17} - 7 q^{18} - 16 q^{19} - q^{20} + 12 q^{22} + 20 q^{23}+ \cdots + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(145))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 29
145.2.a.a 145.a 1.a $1$ $1.158$ \(\Q\) None 145.2.a.a \(-1\) \(0\) \(-1\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}-3q^{9}+\cdots\)
145.2.a.b 145.a 1.a $2$ $1.158$ \(\Q(\sqrt{2}) \) None 145.2.a.b \(-2\) \(-4\) \(2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-2q^{3}+(1-2\beta )q^{4}+\cdots\)
145.2.a.c 145.a 1.a $3$ $1.158$ 3.3.148.1 None 145.2.a.c \(1\) \(2\) \(3\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
145.2.a.d 145.a 1.a $3$ $1.158$ 3.3.148.1 None 145.2.a.d \(3\) \(-2\) \(-3\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(145))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(145)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 2}\)