Properties

Label 49.2.c
Level $49$
Weight $2$
Character orbit 49.c
Rep. character $\chi_{49}(18,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $2$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 49.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(49, [\chi])\).

Total New Old
Modular forms 18 10 8
Cusp forms 2 2 0
Eisenstein series 16 8 8

Trace form

\( 2 q - q^{2} + q^{4} - 6 q^{8} + 3 q^{9} + O(q^{10}) \) \( 2 q - q^{2} + q^{4} - 6 q^{8} + 3 q^{9} - 4 q^{11} + q^{16} + 3 q^{18} + 8 q^{22} - 8 q^{23} + 5 q^{25} + 4 q^{29} - 5 q^{32} + 6 q^{36} + 6 q^{37} - 24 q^{43} + 4 q^{44} - 8 q^{46} - 10 q^{50} + 10 q^{53} - 2 q^{58} + 14 q^{64} - 4 q^{67} + 32 q^{71} - 9 q^{72} + 6 q^{74} - 8 q^{79} - 9 q^{81} + 12 q^{86} + 12 q^{88} - 16 q^{92} - 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
49.2.c.a 49.c 7.c $2$ $0.391$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) 49.2.a.a \(-1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots\)