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Properties

Label 1638.2.cf
Level $1638$
Weight $2$
Character orbit 1638.cf
Rep. character $\chi_{1638}(521,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $4$
Sturm bound $672$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.cf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(672\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1638, [\chi])\).

Total New Old
Modular forms 704 64 640
Cusp forms 640 64 576
Eisenstein series 64 0 64

Trace form

\( 64 q + 32 q^{4} - 8 q^{7} + O(q^{10}) \) \( 64 q + 32 q^{4} - 8 q^{7} - 24 q^{10} - 32 q^{16} + 48 q^{22} - 24 q^{25} + 8 q^{28} + 24 q^{31} - 24 q^{40} - 32 q^{43} - 16 q^{46} + 8 q^{49} - 8 q^{58} - 64 q^{64} + 24 q^{70} + 48 q^{73} - 24 q^{79} + 32 q^{85} + 24 q^{88} + 32 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1638, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1638.2.cf.a 1638.cf 21.g $8$ $13.079$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(-1-\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)
1638.2.cf.b 1638.cf 21.g $8$ $13.079$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{2}+(1-\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
1638.2.cf.c 1638.cf 21.g $24$ $13.079$ None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{6}]$
1638.2.cf.d 1638.cf 21.g $24$ $13.079$ None \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1638, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(819, [\chi])\)\(^{\oplus 2}\)