↑

Properties

Label 945.2.bh
Level $945$
Weight $2$
Character orbit 945.bh
Rep. character $\chi_{945}(64,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $3$
Sturm bound $288$
Trace bound $4$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(288\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(945, [\chi])\).

Total New Old
Modular forms 312 72 240
Cusp forms 264 72 192
Eisenstein series 48 0 48

Trace form

\( 72 q + 36 q^{4} + 2 q^{5} + O(q^{10}) \) \( 72 q + 36 q^{4} + 2 q^{5} - 18 q^{11} + 8 q^{14} - 36 q^{16} + 6 q^{20} + 6 q^{25} + 32 q^{26} + 20 q^{29} - 12 q^{31} + 12 q^{34} - 8 q^{41} - 32 q^{44} + 24 q^{46} + 36 q^{49} + 50 q^{50} - 12 q^{55} - 24 q^{56} + 4 q^{59} - 96 q^{64} + 20 q^{65} + 168 q^{71} + 28 q^{74} - 12 q^{76} - 6 q^{79} - 104 q^{80} - 24 q^{85} - 44 q^{86} + 80 q^{89} - 12 q^{91} - 48 q^{94} - 20 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
945.2.bh.a 945.bh 45.j $4$ $7.546$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{4}+(-\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
945.2.bh.b 945.bh 45.j $4$ $7.546$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{12}q^{2}+2\zeta_{12}^{2}q^{4}+(\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
945.2.bh.c 945.bh 45.j $64$ $7.546$ None \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(945, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)