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Properties

Label 245.2.l
Level $245$
Weight $2$
Character orbit 245.l
Rep. character $\chi_{245}(68,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $64$
Newform subspaces $4$
Sturm bound $56$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.l (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(56\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 144 96 48
Cusp forms 80 64 16
Eisenstein series 64 32 32

Trace form

\( 64 q + 2 q^{2} + 6 q^{3} - 20 q^{8} + O(q^{10}) \) \( 64 q + 2 q^{2} + 6 q^{3} - 20 q^{8} - 6 q^{10} - 8 q^{11} - 6 q^{12} - 12 q^{15} + 4 q^{16} - 12 q^{17} - 36 q^{18} - 48 q^{22} - 14 q^{23} + 20 q^{25} + 24 q^{26} - 20 q^{30} + 24 q^{31} + 62 q^{32} + 56 q^{36} - 8 q^{37} + 12 q^{38} - 18 q^{40} - 4 q^{43} - 24 q^{45} - 52 q^{46} - 24 q^{47} - 92 q^{50} + 20 q^{51} - 24 q^{52} + 24 q^{53} - 72 q^{57} + 70 q^{58} + 10 q^{60} + 24 q^{61} + 40 q^{65} + 12 q^{66} + 22 q^{67} + 12 q^{68} - 88 q^{71} - 8 q^{72} + 24 q^{73} + 6 q^{75} + 120 q^{78} + 24 q^{80} - 60 q^{81} + 6 q^{82} - 32 q^{85} - 52 q^{86} - 18 q^{87} - 16 q^{88} + 28 q^{92} - 48 q^{93} + 60 q^{95} - 60 q^{96} + O(q^{100}) \)

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.l.a 245.l 35.k $4$ $1.956$ \(\Q(\zeta_{12})\) None \(-4\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
245.2.l.b 245.l 35.k $4$ $1.956$ \(\Q(\zeta_{12})\) None \(2\) \(4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots\)
245.2.l.c 245.l 35.k $8$ $1.956$ 8.0.3317760000.2 None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+\beta _{5}q^{5}+\cdots\)
245.2.l.d 245.l 35.k $48$ $1.956$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

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