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Properties

Label 714.2.bl
Level $714$
Weight $2$
Character orbit 714.bl
Rep. character $\chi_{714}(31,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $384$
Newform subspaces $2$
Sturm bound $288$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 714.bl (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 119 \)
Character field: \(\Q(\zeta_{48})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(10\)
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 384 2048
Cusp forms 2176 384 1792
Eisenstein series 256 0 256

Trace form

\( 384 q + O(q^{10}) \) \( 384 q + 32 q^{11} - 32 q^{14} + 64 q^{22} + 32 q^{25} + 64 q^{35} + 32 q^{37} - 32 q^{46} + 128 q^{49} + 32 q^{58} + 96 q^{61} - 128 q^{71} + 96 q^{73} + 128 q^{74} - 32 q^{77} - 128 q^{78} + 96 q^{80} - 128 q^{85} + 288 q^{87} + 32 q^{88} + 64 q^{91} - 64 q^{92} + 192 q^{94} + 128 q^{95} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bl.a 714.bl 119.s $192$ $5.701$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{48}]$
714.2.bl.b 714.bl 119.s $192$ $5.701$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{48}]$

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

\( S_{2}^{\mathrm{old}}(714, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 2}\)