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Properties

Label 650.2.ba
Level $650$
Weight $2$
Character orbit 650.ba
Rep. character $\chi_{650}(73,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $280$
Newform subspaces $2$
Sturm bound $210$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 650.ba (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(210\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 872 280 592
Cusp forms 808 280 528
Eisenstein series 64 0 64

Trace form

\( 280 q + 2 q^{2} - 70 q^{4} + 2 q^{8} + 12 q^{13} + 40 q^{15} - 70 q^{16} - 2 q^{17} - 40 q^{19} + 24 q^{23} + 2 q^{25} + 12 q^{27} + 40 q^{29} + 24 q^{30} - 8 q^{32} - 108 q^{33} + 10 q^{34} - 12 q^{35}+ \cdots + 30 q^{98}+O(q^{100}) \) 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.ba.a 650.ba 325.z $136$ $5.190$ None 650.2.ba.a \(-34\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$
650.2.ba.b 650.ba 325.z $144$ $5.190$ None 650.2.ba.b \(36\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

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

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