Properties

Label 3360.2.d
Level $3360$
Weight $2$
Character orbit 3360.d
Rep. character $\chi_{3360}(2911,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $4$
Sturm bound $1536$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3360.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1536\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3360, [\chi])\).

Total New Old
Modular forms 800 64 736
Cusp forms 736 64 672
Eisenstein series 64 0 64

Trace form

\( 64 q + 64 q^{9} + O(q^{10}) \) \( 64 q + 64 q^{9} - 16 q^{21} - 64 q^{25} - 32 q^{37} - 64 q^{53} - 32 q^{57} - 32 q^{65} - 32 q^{77} + 64 q^{81} + 32 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3360, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3360.2.d.a 3360.d 28.d $16$ $26.830$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta _{5}q^{5}-\beta _{10}q^{7}+q^{9}+(-\beta _{5}+\cdots)q^{11}+\cdots\)
3360.2.d.b 3360.d 28.d $16$ $26.830$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-16\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{3}q^{5}+\beta _{14}q^{7}+q^{9}+\beta _{12}q^{11}+\cdots\)
3360.2.d.c 3360.d 28.d $16$ $26.830$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(16\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta _{3}q^{5}+(-1+\beta _{13})q^{7}+q^{9}+\cdots\)
3360.2.d.d 3360.d 28.d $16$ $26.830$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\beta _{5}q^{5}-\beta _{12}q^{7}+q^{9}+(-\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3360, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)