Properties

Label 145.2.j
Level $145$
Weight $2$
Character orbit 145.j
Rep. character $\chi_{145}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $26$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 145 = 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 145.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 145 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 34 34 0
Cusp forms 26 26 0
Eisenstein series 8 8 0

Trace form

\( 26 q - 6 q^{2} + 22 q^{4} - 4 q^{7} - 18 q^{8} - 10 q^{9} + O(q^{10}) \) \( 26 q - 6 q^{2} + 22 q^{4} - 4 q^{7} - 18 q^{8} - 10 q^{9} - 6 q^{10} - 8 q^{11} + 14 q^{13} - 4 q^{14} + 10 q^{15} + 6 q^{16} + 20 q^{17} - 18 q^{18} - 20 q^{20} + 16 q^{21} - 8 q^{22} - 4 q^{23} + 10 q^{25} + 6 q^{26} - 8 q^{28} + 16 q^{30} + 8 q^{31} - 42 q^{32} - 32 q^{34} - 16 q^{35} - 22 q^{36} - 8 q^{38} - 16 q^{39} - 22 q^{40} - 6 q^{41} - 4 q^{42} - 44 q^{45} - 32 q^{46} + 8 q^{50} + 26 q^{52} + 14 q^{53} + 6 q^{55} - 32 q^{56} - 12 q^{57} + 28 q^{58} + 110 q^{60} + 18 q^{61} + 28 q^{62} + 60 q^{63} + 30 q^{64} - 18 q^{65} + 20 q^{66} + 32 q^{67} + 72 q^{68} + 12 q^{69} - 12 q^{70} + 10 q^{72} - 4 q^{73} + 6 q^{75} + 20 q^{76} - 12 q^{77} + 56 q^{78} + 4 q^{79} - 12 q^{80} - 86 q^{81} - 58 q^{82} - 60 q^{83} + 76 q^{84} + 60 q^{87} - 68 q^{88} - 46 q^{89} + 44 q^{90} - 28 q^{92} - 8 q^{93} + 60 q^{95} + 36 q^{99} + O(q^{100}) \)

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.j.a 145.j 145.j $26$ $1.158$ None 145.2.e.a \(-6\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$