Properties

Label 121.3.b
Level $121$
Weight $3$
Character orbit 121.b
Rep. character $\chi_{121}(120,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $3$
Sturm bound $33$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 121.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(33\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(121, [\chi])\).

Total New Old
Modular forms 28 22 6
Cusp forms 16 14 2
Eisenstein series 12 8 4

Trace form

\( 14 q + 4 q^{3} - 24 q^{4} - 2 q^{5} - 6 q^{9} + O(q^{10}) \) \( 14 q + 4 q^{3} - 24 q^{4} - 2 q^{5} - 6 q^{9} + 18 q^{12} - 4 q^{14} - 14 q^{15} - 28 q^{16} + 8 q^{20} - 50 q^{23} - 4 q^{25} + 60 q^{26} + 58 q^{27} + 34 q^{31} - 38 q^{34} + 26 q^{36} + 30 q^{37} - 14 q^{38} - 116 q^{42} + 12 q^{45} - 80 q^{47} + 150 q^{48} + 82 q^{49} + 120 q^{53} - 32 q^{56} + 4 q^{58} - 140 q^{59} - 192 q^{60} + 84 q^{64} - 8 q^{67} + 222 q^{69} + 32 q^{70} + 154 q^{71} - 234 q^{75} + 28 q^{78} - 284 q^{80} - 298 q^{81} - 22 q^{82} + 34 q^{86} + 80 q^{89} + 20 q^{91} - 132 q^{92} - 134 q^{93} + 108 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(121, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
121.3.b.a 121.b 11.b $2$ $3.297$ \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-q^{3}+2q^{4}-7q^{5}-\beta q^{6}+\cdots\)
121.3.b.b 121.b 11.b $4$ $3.297$ \(\Q(\zeta_{10})\) None \(0\) \(10\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{10}-\zeta_{10}^{3})q^{2}+(2-\zeta_{10}^{2})q^{3}+\cdots\)
121.3.b.c 121.b 11.b $8$ $3.297$ 8.0.\(\cdots\).1 None \(0\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{3}+\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(121, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(121, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)