Properties

Label 245.4.j
Level $245$
Weight $4$
Character orbit 245.j
Rep. character $\chi_{245}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $112$
Newform subspaces $7$
Sturm bound $112$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
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: \(112\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(245, [\chi])\).

Total New Old
Modular forms 184 128 56
Cusp forms 152 112 40
Eisenstein series 32 16 16

Trace form

\( 112 q + 210 q^{4} - 3 q^{5} + 96 q^{6} + 388 q^{9} + 32 q^{10} - 32 q^{11} + 222 q^{15} - 746 q^{16} + 192 q^{19} - 584 q^{20} + 444 q^{24} + 191 q^{25} - 434 q^{26} - 524 q^{29} + 898 q^{30} - 834 q^{31}+ \cdots - 19596 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.4.j.a 245.j 35.j $4$ $14.455$ \(\Q(\sqrt{-3}, \sqrt{-5})\) \(\Q(\sqrt{-35}) \) 245.4.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+4\beta _{1}q^{3}+(-8+8\beta _{2})q^{4}+(5\beta _{1}-5\beta _{3})q^{5}+\cdots\)
245.4.j.b 245.j 35.j $8$ $14.455$ \(\Q(\zeta_{24})\) None 245.4.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta_1 q^{2}+(-4\beta_{6}+2\beta_{4})q^{3}+\beta_{2} q^{4}+\cdots\)
245.4.j.c 245.j 35.j $16$ $14.455$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 245.4.b.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{6}q^{2}+\beta _{14}q^{3}+(1+9\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
245.4.j.d 245.j 35.j $20$ $14.455$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 35.4.j.a \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+\beta _{14}q^{3}+(-\beta _{2}-3\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
245.4.j.e 245.j 35.j $20$ $14.455$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 35.4.b.a \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{12}q^{2}-\beta _{11}q^{3}+(4-4\beta _{1}+\beta _{8}+\cdots)q^{4}+\cdots\)
245.4.j.f 245.j 35.j $20$ $14.455$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 35.4.b.a \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{12}q^{2}+\beta _{11}q^{3}+(4-4\beta _{1}+\beta _{8}+\cdots)q^{4}+\cdots\)
245.4.j.g 245.j 35.j $24$ $14.455$ None 245.4.b.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)