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Properties

Label 49.3.d
Level $49$
Weight $3$
Character orbit 49.d
Rep. character $\chi_{49}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $10$
Newform subspaces $2$
Sturm bound $14$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 49.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(14\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(49, [\chi])\).

Total New Old
Modular forms 26 18 8
Cusp forms 10 10 0
Eisenstein series 16 8 8

Trace form

\( 10 q - q^{2} - q^{4} - 14 q^{8} - 5 q^{9} + O(q^{10}) \) \( 10 q - q^{2} - q^{4} - 14 q^{8} - 5 q^{9} - 2 q^{11} - 16 q^{15} + 23 q^{16} + 23 q^{18} - 28 q^{22} + 6 q^{23} - 45 q^{25} + 20 q^{29} - 72 q^{30} + 47 q^{32} + 130 q^{36} + 6 q^{37} - 56 q^{39} + 132 q^{43} + 118 q^{44} + 14 q^{46} - 78 q^{50} - 72 q^{51} + 110 q^{53} - 352 q^{57} - 114 q^{58} - 168 q^{60} - 318 q^{64} + 224 q^{65} + 166 q^{67} - 92 q^{71} + 47 q^{72} - 210 q^{74} + 560 q^{78} - 274 q^{79} + 267 q^{81} + 656 q^{85} - 2 q^{86} - 130 q^{88} + 484 q^{92} + 208 q^{93} - 200 q^{95} - 204 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
49.3.d.a 49.d 7.d $2$ $1.335$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) \(3\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+3\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{4}-3q^{8}+\cdots\)
49.3.d.b 49.d 7.d $8$ $1.335$ 8.0.339738624.1 None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{4}-\beta _{5})q^{2}+\beta _{1}q^{3}+(1+2\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)