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Properties

Label 290.2.d
Level $290$
Weight $2$
Character orbit 290.d
Rep. character $\chi_{290}(289,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $90$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 290 = 2 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 290.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 145 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(90\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 48 16 32
Cusp forms 40 16 24
Eisenstein series 8 0 8

Trace form

\( 16 q + 16 q^{4} - 2 q^{5} - 8 q^{6} + 16 q^{9} + 16 q^{16} - 2 q^{20} - 8 q^{24} + 10 q^{25} - 8 q^{29} - 6 q^{30} - 4 q^{34} + 16 q^{36} - 8 q^{45} - 12 q^{49} - 48 q^{51} - 20 q^{54} - 36 q^{59} + 16 q^{64}+ \cdots - 8 q^{96}+O(q^{100}) \) Copy content Toggle raw display

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.d.a 290.d 145.d $8$ $2.316$ 8.0.\(\cdots\).1 None 290.2.d.a \(-8\) \(4\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots\)
290.2.d.b 290.d 145.d $8$ $2.316$ 8.0.\(\cdots\).1 None 290.2.d.a \(8\) \(-4\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots\)

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

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