Properties

Label 2340.2.j
Level $2340$
Weight $2$
Character orbit 2340.j
Rep. character $\chi_{2340}(649,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $5$
Sturm bound $1008$
Trace bound $25$

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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.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(1008\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 528 36 492
Cusp forms 480 36 444
Eisenstein series 48 0 48

Trace form

\( 36 q + O(q^{10}) \) \( 36 q - 4 q^{25} - 8 q^{29} - 8 q^{35} + 44 q^{49} - 16 q^{55} - 8 q^{61} + 16 q^{65} - 8 q^{79} + 32 q^{91} + 24 q^{95} + O(q^{100}) \)

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.j.a 2340.j 65.d $4$ $18.685$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}-2q^{7}+\zeta_{8}^{2}q^{11}+\cdots\)
2340.2.j.b 2340.j 65.d $4$ $18.685$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}+2q^{7}+\zeta_{8}^{2}q^{11}+\cdots\)
2340.2.j.c 2340.j 65.d $8$ $18.685$ 8.0.4569760000.1 \(\Q(\sqrt{-195}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{5}q^{5}+\beta _{1}q^{7}+(-\beta _{2}-\beta _{5})q^{11}+\cdots\)
2340.2.j.d 2340.j 65.d $8$ $18.685$ 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{5}+(-\beta _{5}+\beta _{6})q^{7}-\beta _{7}q^{11}+\cdots\)
2340.2.j.e 2340.j 65.d $12$ $18.685$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{11}q^{5}+\beta _{10}q^{7}+\beta _{9}q^{11}+(-\beta _{4}+\cdots)q^{13}+\cdots\)

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

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