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Properties

Label 650.2.r
Level $650$
Weight $2$
Character orbit 650.r
Rep. character $\chi_{650}(129,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $144$
Newform subspaces $2$
Sturm bound $210$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 650.r (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(210\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(650, [\chi])\).

Total New Old
Modular forms 432 144 288
Cusp forms 400 144 256
Eisenstein series 32 0 32

Trace form

\( 144 q - 36 q^{4} + 40 q^{9} + 6 q^{10} + 8 q^{14} - 36 q^{16} - 20 q^{23} - 42 q^{25} + 6 q^{26} + 36 q^{29} + 2 q^{30} + 30 q^{35} + 40 q^{36} + 32 q^{39} + 6 q^{40} + 176 q^{49} - 84 q^{51} - 70 q^{53}+ \cdots + 36 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(650, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
650.2.r.a 650.r 325.p $72$ $5.190$ None 650.2.r.a \(-18\) \(0\) \(3\) \(-16\) $\mathrm{SU}(2)[C_{10}]$
650.2.r.b 650.r 325.p $72$ $5.190$ None 650.2.r.a \(18\) \(0\) \(-3\) \(16\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(650, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)