↑

Properties

Label 735.2.bt
Level $735$
Weight $2$
Character orbit 735.bt
Rep. character $\chi_{735}(2,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $2592$
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.bt (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 735 \)
Character field: \(\Q(\zeta_{84})\)
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 2784 2784 0
Cusp forms 2592 2592 0
Eisenstein series 192 192 0

Trace form

\( 2592 q - 26 q^{3} - 60 q^{6} - 44 q^{7} + O(q^{10}) \) \( 2592 q - 26 q^{3} - 60 q^{6} - 44 q^{7} - 48 q^{10} - 18 q^{12} - 40 q^{13} - 32 q^{15} - 296 q^{16} - 20 q^{18} - 28 q^{21} - 4 q^{22} - 52 q^{25} - 68 q^{27} + 4 q^{28} - 34 q^{30} - 32 q^{31} - 24 q^{33} + 52 q^{36} - 52 q^{37} - 40 q^{40} + 70 q^{42} - 72 q^{43} - 180 q^{45} - 416 q^{46} - 100 q^{48} - 52 q^{51} - 92 q^{52} - 16 q^{55} + 12 q^{57} - 284 q^{58} - 22 q^{60} - 216 q^{61} - 72 q^{63} + 64 q^{66} - 40 q^{67} - 84 q^{70} - 54 q^{72} - 108 q^{73} + 50 q^{75} - 400 q^{76} + 108 q^{78} - 276 q^{81} - 300 q^{82} - 16 q^{85} + 18 q^{87} - 104 q^{88} + 140 q^{90} + 40 q^{91} - 196 q^{93} + 184 q^{96} + 8 q^{97} + O(q^{100}) \)

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.bt.a 735.bt 735.at $2592$ $5.869$ None \(0\) \(-26\) \(0\) \(-44\) $\mathrm{SU}(2)[C_{84}]$