↑

Properties

Label 735.2.bj
Level $735$
Weight $2$
Character orbit 735.bj
Rep. character $\chi_{735}(8,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1296$
Newform subspaces $1$
Sturm bound $224$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.bj (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 735 \)
Character field: \(\Q(\zeta_{28})\)
Newform subspaces: \( 1 \)
Sturm bound: \(224\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(735, [\chi])\).

Total New Old
Modular forms 1392 1392 0
Cusp forms 1296 1296 0
Eisenstein series 96 96 0

Trace form

\( 1296 q - 10 q^{3} - 28 q^{7} + O(q^{10}) \) \( 1296 q - 10 q^{3} - 28 q^{7} - 12 q^{10} - 30 q^{12} - 20 q^{13} + 2 q^{15} + 152 q^{16} - 16 q^{18} - 32 q^{21} - 56 q^{22} - 20 q^{25} + 2 q^{27} - 28 q^{28} - 68 q^{30} - 112 q^{31} - 42 q^{33} - 112 q^{36} - 20 q^{37} - 92 q^{40} - 106 q^{42} + 12 q^{43} + 78 q^{45} - 160 q^{46} - 44 q^{48} - 20 q^{51} - 28 q^{52} - 68 q^{55} - 42 q^{57} + 104 q^{58} - 2 q^{60} - 144 q^{61} - 6 q^{63} - 208 q^{66} - 80 q^{67} - 132 q^{70} + 54 q^{72} - 60 q^{73} - 38 q^{75} + 136 q^{76} - 66 q^{78} + 120 q^{81} + 192 q^{82} - 44 q^{85} - 18 q^{87} - 76 q^{88} - 74 q^{90} - 256 q^{91} - 230 q^{93} - 184 q^{96} - 80 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(735, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
735.2.bj.a 735.bj 735.aj $1296$ $5.869$ None \(0\) \(-10\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{28}]$