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Properties

Label 2340.2.q
Level $2340$
Weight $2$
Character orbit 2340.q
Rep. character $\chi_{2340}(1621,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $11$
Sturm bound $1008$
Trace bound $11$

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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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 11 \)
Sturm bound: \(1008\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(19\)

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

\( 48 q - 2 q^{7} + O(q^{10}) \) \( 48 q - 2 q^{7} + 4 q^{11} - 2 q^{17} - 4 q^{19} - 2 q^{23} + 48 q^{25} - 4 q^{29} - 24 q^{31} - 6 q^{35} - 6 q^{37} - 4 q^{41} + 6 q^{43} - 56 q^{47} - 24 q^{49} + 8 q^{53} + 8 q^{55} - 8 q^{59} + 20 q^{61} + 8 q^{65} + 22 q^{67} + 24 q^{71} - 32 q^{73} - 12 q^{77} - 32 q^{79} + 48 q^{83} + 6 q^{85} + 32 q^{89} - 12 q^{91} + 18 q^{97} + O(q^{100}) \)

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.q.a 2340.q 13.c $2$ $18.685$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{5}-3\zeta_{6}q^{7}+(3-3\zeta_{6})q^{11}+(-1+\cdots)q^{13}+\cdots\)
2340.2.q.b 2340.q 13.c $2$ $18.685$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{5}+\zeta_{6}q^{7}+(3-3\zeta_{6})q^{11}+(3-4\zeta_{6})q^{13}+\cdots\)
2340.2.q.c 2340.q 13.c $2$ $18.685$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{5}-5\zeta_{6}q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
2340.2.q.d 2340.q 13.c $2$ $18.685$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{5}-3\zeta_{6}q^{7}+(6-6\zeta_{6})q^{11}+(-4+\cdots)q^{13}+\cdots\)
2340.2.q.e 2340.q 13.c $2$ $18.685$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{5}+\zeta_{6}q^{7}+(-2+2\zeta_{6})q^{11}+(4+\cdots)q^{13}+\cdots\)
2340.2.q.f 2340.q 13.c $2$ $18.685$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{5}+\zeta_{6}q^{7}+(3-3\zeta_{6})q^{11}+(-1+\cdots)q^{13}+\cdots\)
2340.2.q.g 2340.q 13.c $4$ $18.685$ \(\Q(\sqrt{-3}, \sqrt{10})\) None \(0\) \(0\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+2\beta _{2}q^{11}+\cdots\)
2340.2.q.h 2340.q 13.c $6$ $18.685$ 6.0.31259952.1 None \(0\) \(0\) \(-6\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{5}+(-\beta _{4}+\beta _{5})q^{7}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
2340.2.q.i 2340.q 13.c $6$ $18.685$ 6.0.16765488.1 None \(0\) \(0\) \(6\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{5}+(\beta _{1}-\beta _{5})q^{7}+(1+\beta _{2})q^{13}+\cdots\)
2340.2.q.j 2340.q 13.c $10$ $18.685$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-10\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{5}+\beta _{8}q^{7}+(-1+\beta _{1}-\beta _{7}+\beta _{9})q^{11}+\cdots\)
2340.2.q.k 2340.q 13.c $10$ $18.685$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(10\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{5}+\beta _{8}q^{7}+(1-\beta _{1}+\beta _{7}-\beta _{9})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)