Properties

Label 290.2.b
Level $290$
Weight $2$
Character orbit 290.b
Rep. character $\chi_{290}(59,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $2$
Sturm bound $90$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 290 = 2 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 290.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(90\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(290, [\chi])\).

Total New Old
Modular forms 50 14 36
Cusp forms 42 14 28
Eisenstein series 8 0 8

Trace form

\( 14 q - 14 q^{4} - 22 q^{9} + O(q^{10}) \) \( 14 q - 14 q^{4} - 22 q^{9} + 8 q^{11} - 4 q^{14} + 8 q^{15} + 14 q^{16} + 16 q^{19} - 8 q^{21} - 24 q^{25} + 8 q^{26} - 6 q^{29} - 6 q^{30} + 8 q^{31} + 8 q^{35} + 22 q^{36} - 24 q^{39} - 4 q^{41} - 8 q^{44} + 26 q^{45} + 20 q^{46} - 18 q^{49} - 16 q^{50} - 32 q^{51} + 12 q^{54} + 16 q^{55} + 4 q^{56} + 20 q^{59} - 8 q^{60} - 20 q^{61} - 14 q^{64} + 10 q^{65} + 24 q^{66} - 8 q^{69} - 20 q^{70} - 8 q^{71} + 12 q^{74} + 20 q^{75} - 16 q^{76} + 48 q^{79} - 2 q^{81} + 8 q^{84} + 28 q^{85} - 16 q^{86} - 28 q^{89} - 4 q^{90} - 40 q^{91} - 4 q^{94} - 8 q^{95} + 64 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(290, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
290.2.b.a 290.b 5.b $4$ $2.316$ \(\Q(i, \sqrt{5})\) None 290.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+(-\beta _{1}+\beta _{3})q^{3}-q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
290.2.b.b 290.b 5.b $10$ $2.316$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None 290.2.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{5})q^{3}-q^{4}+\beta _{3}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(290, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(290, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)