Properties

Label 145.2.b
Level $145$
Weight $2$
Character orbit 145.b
Rep. character $\chi_{145}(59,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $3$
Sturm bound $30$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 145 = 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 145.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(30\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(145, [\chi])\).

Total New Old
Modular forms 18 14 4
Cusp forms 14 14 0
Eisenstein series 4 0 4

Trace form

\( 14 q - 18 q^{4} + 4 q^{6} - 10 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{14} - 2 q^{15} + 18 q^{16} - 12 q^{19} + 4 q^{20} - 28 q^{24} + 16 q^{25} - 4 q^{26} + 6 q^{29} + 34 q^{30} - 8 q^{31} - 28 q^{34} + 8 q^{35}+ \cdots - 68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(145, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
145.2.b.a 145.b 5.b $4$ $1.158$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None 145.2.b.a \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{3})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
145.2.b.b 145.b 5.b $4$ $1.158$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 145.2.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
145.2.b.c 145.b 5.b $6$ $1.158$ 6.0.84345856.2 None 145.2.b.c \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-3+\beta _{3}+\cdots)q^{4}+\cdots\)