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

\( 14 q - 18 q^{4} + 4 q^{6} - 10 q^{9} + O(q^{10}) \) \( 14 q - 18 q^{4} + 4 q^{6} - 10 q^{9} + 2 q^{10} - 8 q^{11} + 8 q^{14} - 2 q^{15} + 18 q^{16} - 12 q^{19} + 4 q^{20} - 28 q^{24} + 16 q^{25} - 4 q^{26} + 6 q^{29} + 34 q^{30} - 8 q^{31} - 28 q^{34} + 8 q^{35} - 10 q^{36} + 36 q^{39} + 34 q^{40} + 4 q^{41} - 26 q^{45} - 40 q^{46} - 22 q^{49} + 14 q^{50} + 24 q^{51} - 20 q^{54} - 26 q^{55} + 16 q^{56} - 40 q^{59} + 26 q^{60} + 20 q^{61} - 26 q^{64} + 18 q^{65} + 4 q^{66} + 32 q^{69} + 48 q^{70} + 16 q^{71} + 4 q^{74} - 6 q^{75} - 20 q^{76} - 40 q^{79} - 64 q^{80} - 18 q^{81} + 40 q^{84} - 20 q^{85} - 36 q^{86} + 12 q^{89} - 24 q^{90} + 56 q^{91} + 20 q^{94} - 4 q^{95} + 28 q^{96} - 68 q^{99} + O(q^{100}) \)

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

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