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Properties

Label 1260.2.cj
Level $1260$
Weight $2$
Character orbit 1260.cj
Rep. character $\chi_{1260}(209,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $3$
Sturm bound $576$
Trace bound $11$

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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.cj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(576\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

Total New Old
Modular forms 600 96 504
Cusp forms 552 96 456
Eisenstein series 48 0 48

Trace form

\( 96 q + O(q^{10}) \) \( 96 q + 6 q^{11} + 2 q^{15} + 16 q^{21} + 12 q^{29} + 42 q^{39} + 6 q^{49} + 26 q^{51} + 54 q^{65} + 18 q^{79} + 40 q^{81} + 60 q^{95} - 16 q^{99} + O(q^{100}) \)

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.cj.a 1260.cj 315.z $8$ $10.061$ 8.0.\(\cdots\).2 \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{3}+\beta _{5}-\beta _{6})q^{5}+\cdots\)
1260.2.cj.b 1260.cj 315.z $8$ $10.061$ 8.0.\(\cdots\).2 \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(\beta _{1}+\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
1260.2.cj.c 1260.cj 315.z $80$ $10.061$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)