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Properties

Label 245.2.e
Level $245$
Weight $2$
Character orbit 245.e
Rep. character $\chi_{245}(116,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $28$
Newform subspaces $9$
Sturm bound $56$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 9 \)
Sturm bound: \(56\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

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

Total New Old
Modular forms 72 28 44
Cusp forms 40 28 12
Eisenstein series 32 0 32

Trace form

\( 28 q + 4 q^{2} + 2 q^{3} - 12 q^{4} + 2 q^{5} + 4 q^{6} - 24 q^{8} - 14 q^{9} + 2 q^{10} + 10 q^{11} - 6 q^{12} + 8 q^{13} - 8 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{20} - 16 q^{22} + 2 q^{23} + 2 q^{24}+ \cdots + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.2.e.a 245.e 7.c $2$ $1.956$ \(\Q(\sqrt{-3}) \) None 35.2.a.a \(0\) \(-1\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
245.2.e.b 245.e 7.c $2$ $1.956$ \(\Q(\sqrt{-3}) \) None 35.2.a.a \(0\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
245.2.e.c 245.e 7.c $2$ $1.956$ \(\Q(\sqrt{-3}) \) None 245.2.a.a \(2\) \(-3\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
245.2.e.d 245.e 7.c $2$ $1.956$ \(\Q(\sqrt{-3}) \) None 245.2.a.a \(2\) \(3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
245.2.e.e 245.e 7.c $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 35.2.e.a \(-2\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
245.2.e.f 245.e 7.c $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 245.2.a.e \(0\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-1+\cdots)q^{5}+\cdots\)
245.2.e.g 245.e 7.c $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 245.2.a.e \(0\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
245.2.e.h 245.e 7.c $4$ $1.956$ \(\Q(\sqrt{-3}, \sqrt{17})\) None 35.2.a.b \(1\) \(-1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
245.2.e.i 245.e 7.c $4$ $1.956$ \(\Q(\sqrt{-3}, \sqrt{17})\) None 35.2.a.b \(1\) \(1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)