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Properties

Label 2340.2.cr
Level $2340$
Weight $2$
Character orbit 2340.cr
Rep. character $\chi_{2340}(829,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $3$
Sturm bound $1008$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2340.cr (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(1008\)
Trace bound: \(1\)
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 72 984
Cusp forms 960 72 888
Eisenstein series 96 0 96

Trace form

\( 72 q + O(q^{10}) \) \( 72 q - 6 q^{11} + 6 q^{19} - 2 q^{25} - 16 q^{29} + 2 q^{35} - 24 q^{41} - 50 q^{49} - 14 q^{55} - 6 q^{59} - 16 q^{61} + 5 q^{65} + 6 q^{71} - 16 q^{79} + 21 q^{85} - 30 q^{89} + 22 q^{91} + 24 q^{95} + O(q^{100}) \)

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.cr.a 2340.cr 65.l $16$ $18.685$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{12}q^{5}+\beta _{8}q^{7}+(\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{11}+\cdots\)
2340.2.cr.b 2340.cr 65.l $24$ $18.685$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
2340.2.cr.c 2340.cr 65.l $32$ $18.685$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)