Properties

Label 49.3.b
Level $49$
Weight $3$
Character orbit 49.b
Rep. character $\chi_{49}(48,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $14$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 49.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 14 8 6
Cusp forms 6 4 2
Eisenstein series 8 4 4

Trace form

\( 4 q + 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{9} + 8 q^{11} - 8 q^{15} - 12 q^{16} + 4 q^{18} - 32 q^{22} - 24 q^{23} + 20 q^{25} + 64 q^{29} + 72 q^{30} - 92 q^{32} + 20 q^{36} + 32 q^{37} + 56 q^{39} + 8 q^{43} - 88 q^{44} + 40 q^{46} + 36 q^{50} + 72 q^{51} - 104 q^{53} - 176 q^{57} - 48 q^{58} + 168 q^{60} - 68 q^{64} - 224 q^{65} - 48 q^{67} - 160 q^{71} - 20 q^{72} + 96 q^{74} + 280 q^{78} + 368 q^{79} - 348 q^{81} + 328 q^{85} + 176 q^{86} + 112 q^{88} + 152 q^{92} - 208 q^{93} + 200 q^{95} - 48 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
49.3.b.a 49.b 7.b $4$ $1.335$ 4.0.2048.2 None 49.3.b.a \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{2})q^{2}-\beta _{3}q^{3}+(-1+2\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(49, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(49, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)