↑

Properties

Label 696.2.bd
Level $696$
Weight $2$
Character orbit 696.bd
Rep. character $\chi_{696}(35,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $696$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 696.bd (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 696 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(696, [\chi])\).

Total New Old
Modular forms 744 744 0
Cusp forms 696 696 0
Eisenstein series 48 48 0

Trace form

\( 696 q - 14 q^{3} - 10 q^{4} + 5 q^{6} - 10 q^{9} + O(q^{10}) \) \( 696 q - 14 q^{3} - 10 q^{4} + 5 q^{6} - 10 q^{9} - 14 q^{10} - 26 q^{16} + 42 q^{18} - 28 q^{19} + 8 q^{22} - 13 q^{24} - 120 q^{25} - 14 q^{27} + 28 q^{28} + 2 q^{30} + 2 q^{33} - 20 q^{34} + 9 q^{36} - 14 q^{40} + 40 q^{42} - 28 q^{43} - 28 q^{48} + 72 q^{49} - 40 q^{51} - 108 q^{52} - 23 q^{54} - 36 q^{57} + 46 q^{58} + 28 q^{60} - 58 q^{64} - 7 q^{66} + 44 q^{67} - 84 q^{72} - 28 q^{73} + 56 q^{76} - 21 q^{78} + 6 q^{81} - 46 q^{82} - 77 q^{84} + 20 q^{88} + 119 q^{90} - 100 q^{91} - 84 q^{94} - 16 q^{96} - 28 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(696, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
696.2.bd.a 696.bd 696.ad $696$ $5.558$ None \(0\) \(-14\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$