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Properties

Label 1260.2.cg
Level $1260$
Weight $2$
Character orbit 1260.cg
Rep. character $\chi_{1260}(341,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $2$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.cg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1260, [\chi])\).

Total New Old
Modular forms 624 24 600
Cusp forms 528 24 504
Eisenstein series 96 0 96

Trace form

\( 24 q + 4 q^{7} + O(q^{10}) \) \( 24 q + 4 q^{7} - 12 q^{19} - 12 q^{25} - 12 q^{31} - 4 q^{37} + 72 q^{43} + 44 q^{49} + 4 q^{67} + 12 q^{73} + 28 q^{79} + 20 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1260.2.cg.a 1260.cg 21.g $12$ $10.061$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{4}q^{5}+\beta _{1}q^{7}+(1-\beta _{2}-\beta _{4}-\beta _{6}+\cdots)q^{11}+\cdots\)
1260.2.cg.b 1260.cg 21.g $12$ $10.061$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(6\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{4})q^{5}-\beta _{2}q^{7}+(-2-\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)