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Properties

Label 245.3.c
Level $245$
Weight $3$
Character orbit 245.c
Rep. character $\chi_{245}(244,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $2$
Sturm bound $84$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 245.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(84\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(245, [\chi])\).

Total New Old
Modular forms 64 44 20
Cusp forms 48 36 12
Eisenstein series 16 8 8

Trace form

\( 36 q - 60 q^{4} + 100 q^{9} - 36 q^{11} + 16 q^{15} + 108 q^{16} + 52 q^{25} - 152 q^{29} - 280 q^{30} + 116 q^{36} - 56 q^{39} + 228 q^{44} - 52 q^{46} + 352 q^{50} - 208 q^{51} + 8 q^{60} - 732 q^{64}+ \cdots - 500 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.3.c.a 245.c 35.c $12$ $6.676$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 35.3.i.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{9}q^{3}+(-1+\beta _{1})q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
245.3.c.b 245.c 35.c $24$ $6.676$ None 245.3.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

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