Properties

Label 99.3.k
Level $99$
Weight $3$
Character orbit 99.k
Rep. character $\chi_{99}(19,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $36$
Newform subspaces $3$
Sturm bound $36$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.k (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(99, [\chi])\).

Total New Old
Modular forms 112 44 68
Cusp forms 80 36 44
Eisenstein series 32 8 24

Trace form

\( 36 q + 5 q^{2} + 7 q^{4} + 8 q^{5} + 10 q^{7} + 25 q^{8} + O(q^{10}) \) \( 36 q + 5 q^{2} + 7 q^{4} + 8 q^{5} + 10 q^{7} + 25 q^{8} + 9 q^{11} - 20 q^{13} + 12 q^{14} - 141 q^{16} + 10 q^{17} + 25 q^{19} - 86 q^{20} + 97 q^{22} - 112 q^{23} - 67 q^{25} - 36 q^{26} - 160 q^{28} - 120 q^{29} + 82 q^{31} + 90 q^{34} + 240 q^{35} + 54 q^{37} + 190 q^{38} + 420 q^{40} + 200 q^{41} + 182 q^{44} - 290 q^{46} + 180 q^{47} + 47 q^{49} - 285 q^{50} - 570 q^{52} - 462 q^{53} - 308 q^{55} - 624 q^{56} - 440 q^{58} - 133 q^{59} + 130 q^{61} - 240 q^{62} + 787 q^{64} + 106 q^{67} + 180 q^{68} + 568 q^{70} + 88 q^{71} - 220 q^{73} + 1000 q^{74} + 590 q^{77} + 310 q^{79} + 890 q^{80} + 229 q^{82} - 35 q^{83} - 240 q^{85} - 911 q^{86} - 401 q^{88} - 198 q^{89} - 176 q^{91} + 110 q^{92} + 800 q^{94} - 330 q^{95} + 351 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(99, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
99.3.k.a 99.k 11.d $4$ $2.698$ \(\Q(\zeta_{10})\) None \(5\) \(0\) \(4\) \(10\) $\mathrm{SU}(2)[C_{10}]$ \(q+(2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(-4+\cdots)q^{4}+\cdots\)
99.3.k.b 99.k 11.d $16$ $2.698$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(30\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{5}q^{2}+(-1-3\beta _{2}-\beta _{4}-\beta _{6}+\beta _{11}+\cdots)q^{4}+\cdots\)
99.3.k.c 99.k 11.d $16$ $2.698$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(4\) \(-30\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-1-\beta _{2}+\beta _{5}-\beta _{7}-\beta _{8})q^{2}+(-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(99, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(99, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)