Properties

Label 245.6.b
Level $245$
Weight $6$
Character orbit 245.b
Rep. character $\chi_{245}(99,\cdot)$
Character field $\Q$
Dimension $98$
Newform subspaces $7$
Sturm bound $168$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 245.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(168\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(245, [\chi])\).

Total New Old
Modular forms 148 108 40
Cusp forms 132 98 34
Eisenstein series 16 10 6

Trace form

\( 98 q - 1492 q^{4} - 66 q^{5} - 84 q^{6} - 7270 q^{9} - 464 q^{10} + 464 q^{11} + 1032 q^{15} + 18092 q^{16} + 1592 q^{19} + 2492 q^{20} + 19032 q^{24} - 2694 q^{25} - 13492 q^{26} - 12040 q^{29} + 3116 q^{30}+ \cdots - 62184 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.6.b.a 245.b 5.b $2$ $39.294$ \(\Q(\sqrt{-11}) \) None 5.6.b.a \(0\) \(0\) \(90\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}-3\beta q^{3}-12q^{4}+(45+5\beta )q^{5}+\cdots\)
245.6.b.b 245.b 5.b $2$ $39.294$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-35}) \) 245.6.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}+2^{5}q^{4}-5\beta q^{5}+118q^{9}+\cdots\)
245.6.b.c 245.b 5.b $12$ $39.294$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 245.6.b.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{4}q^{3}+(-20+\beta _{1})q^{4}+\cdots\)
245.6.b.d 245.b 5.b $14$ $39.294$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 35.6.b.a \(0\) \(0\) \(-156\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-\beta _{6}q^{3}+(-15+\beta _{1})q^{4}+\cdots\)
245.6.b.e 245.b 5.b $18$ $39.294$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 35.6.j.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-14+\beta _{2})q^{4}+\cdots\)
245.6.b.f 245.b 5.b $18$ $39.294$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 35.6.j.a \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-14+\beta _{2})q^{4}+\cdots\)
245.6.b.g 245.b 5.b $32$ $39.294$ None 245.6.b.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)