Properties

Label 714.2.bk
Level $714$
Weight $2$
Character orbit 714.bk
Rep. character $\chi_{714}(11,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $768$
Newform subspaces $2$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 714.bk (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 357 \)
Character field: \(\Q(\zeta_{48})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(714, [\chi])\).

Total New Old
Modular forms 2432 768 1664
Cusp forms 2176 768 1408
Eisenstein series 256 0 256

Trace form

\( 768 q + O(q^{10}) \) \( 768 q + 96 q^{15} - 32 q^{18} + 48 q^{21} - 32 q^{37} - 32 q^{39} + 96 q^{42} - 32 q^{46} + 128 q^{49} - 64 q^{51} - 128 q^{55} - 32 q^{58} - 32 q^{60} + 144 q^{63} + 64 q^{69} - 128 q^{73} - 48 q^{75} + 256 q^{85} - 96 q^{87} + 32 q^{88} - 64 q^{91} - 64 q^{93} - 64 q^{94} + 192 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(714, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
714.2.bk.a 714.bk 357.am $384$ $5.701$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{48}]$
714.2.bk.b 714.bk 357.am $384$ $5.701$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{48}]$

Decomposition of \(S_{2}^{\mathrm{old}}(714, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(714, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)