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Properties

Label 245.2.j
Level $245$
Weight $2$
Character orbit 245.j
Rep. character $\chi_{245}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $7$
Sturm bound $56$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 7 \)
Sturm bound: \(56\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(245, [\chi])\).

Total New Old
Modular forms 72 48 24
Cusp forms 40 32 8
Eisenstein series 32 16 16

Trace form

\( 32 q + 14 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{9} + O(q^{10}) \) \( 32 q + 14 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{9} + 4 q^{10} - 2 q^{11} - 28 q^{15} - 2 q^{16} - 12 q^{19} - 4 q^{20} - 6 q^{24} - 8 q^{25} + 4 q^{26} + 8 q^{29} - 30 q^{30} + 4 q^{31} + 8 q^{34} - 80 q^{36} + 6 q^{39} + 12 q^{40} - 20 q^{41} + 68 q^{44} + 4 q^{45} - 34 q^{46} + 24 q^{50} - 50 q^{51} - 10 q^{54} - 20 q^{59} - 48 q^{60} + 14 q^{61} + 76 q^{64} - 42 q^{65} + 12 q^{69} - 8 q^{71} + 48 q^{74} + 8 q^{75} + 24 q^{76} + 10 q^{79} - 2 q^{80} + 48 q^{81} + 4 q^{85} + 18 q^{86} - 18 q^{89} - 16 q^{90} + 20 q^{95} - 10 q^{96} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.2.j.a 245.j 35.j $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-6\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(4+4\beta _{2}+\cdots)q^{4}+\cdots\)
245.2.j.b 245.j 35.j $4$ $1.956$ \(\Q(\sqrt{-3}, \sqrt{-5})\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{3}+(-2+2\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
245.2.j.c 245.j 35.j $4$ $1.956$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
245.2.j.d 245.j 35.j $4$ $1.956$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
245.2.j.e 245.j 35.j $4$ $1.956$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
245.2.j.f 245.j 35.j $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(6\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(4+4\beta _{2}+\cdots)q^{4}+\cdots\)
245.2.j.g 245.j 35.j $8$ $1.956$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(2\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(245, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)