Properties

Label 770.2.w
Level $770$
Weight $2$
Character orbit 770.w
Rep. character $\chi_{770}(139,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $192$
Newform subspaces $2$
Sturm bound $288$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(770, [\chi])\).

Total New Old
Modular forms 608 192 416
Cusp forms 544 192 352
Eisenstein series 64 0 64

Trace form

\( 192 q - 48 q^{4} - 36 q^{9} + O(q^{10}) \) \( 192 q - 48 q^{4} - 36 q^{9} + 8 q^{11} - 6 q^{14} - 12 q^{15} - 48 q^{16} - 4 q^{25} + 60 q^{35} - 56 q^{36} + 20 q^{39} - 32 q^{44} + 74 q^{49} - 60 q^{51} + 4 q^{56} + 8 q^{60} - 48 q^{64} + 48 q^{70} - 40 q^{71} - 252 q^{81} + 160 q^{85} - 72 q^{86} - 62 q^{91} - 60 q^{95} + 200 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(770, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
770.2.w.a 770.w 385.v $96$ $6.148$ None \(-24\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{10}]$
770.2.w.b 770.w 385.v $96$ $6.148$ None \(24\) \(0\) \(0\) \(3\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(770, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)