↑

Properties

Label 2340.2.dj
Level $2340$
Weight $2$
Character orbit 2340.dj
Rep. character $\chi_{2340}(361,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $5$
Sturm bound $1008$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2340.dj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(1008\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2340, [\chi])\).

Total New Old
Modular forms 1056 48 1008
Cusp forms 960 48 912
Eisenstein series 96 0 96

Trace form

\( 48 q - 6 q^{7} + O(q^{10}) \) \( 48 q - 6 q^{7} + 12 q^{11} - 4 q^{13} - 10 q^{17} - 6 q^{23} - 48 q^{25} + 8 q^{29} + 2 q^{35} - 18 q^{37} - 12 q^{41} - 10 q^{43} + 20 q^{49} - 56 q^{53} - 4 q^{65} + 6 q^{67} + 36 q^{71} + 44 q^{77} + 24 q^{79} + 18 q^{85} + 48 q^{89} - 4 q^{91} + 8 q^{95} - 18 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2340, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2340.2.dj.a 2340.dj 13.e $4$ $18.685$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+(-4+2\zeta_{12}^{2}+\cdots)q^{11}+\cdots\)
2340.2.dj.b 2340.dj 13.e $8$ $18.685$ 8.0.454201344.7 None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{4}-\beta _{5})q^{5}+(-1-\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
2340.2.dj.c 2340.dj 13.e $8$ $18.685$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}^{6}q^{5}+(\zeta_{24}+2\zeta_{24}^{2}+\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
2340.2.dj.d 2340.dj 13.e $8$ $18.685$ 8.0.22581504.2 None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{6})q^{5}+(1+\beta _{5}-2\beta _{6})q^{7}+\cdots\)
2340.2.dj.e 2340.dj 13.e $20$ $18.685$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{5}-\beta _{7}q^{7}+(\beta _{15}+\beta _{17})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2340, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)