Properties

Label 105.3.n
Level $105$
Weight $3$
Character orbit 105.n
Rep. character $\chi_{105}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(105, [\chi])\).

Total New Old
Modular forms 72 20 52
Cusp forms 56 20 36
Eisenstein series 16 0 16

Trace form

\( 20 q + 4 q^{2} + 6 q^{3} - 28 q^{4} + 6 q^{7} + 8 q^{8} + 30 q^{9} + O(q^{10}) \) \( 20 q + 4 q^{2} + 6 q^{3} - 28 q^{4} + 6 q^{7} + 8 q^{8} + 30 q^{9} + 40 q^{11} - 48 q^{12} + 16 q^{14} - 84 q^{16} - 96 q^{17} - 12 q^{18} - 6 q^{19} + 84 q^{21} + 40 q^{22} + 64 q^{23} + 108 q^{24} + 50 q^{25} + 156 q^{26} - 248 q^{28} - 200 q^{29} - 18 q^{31} - 72 q^{32} - 60 q^{35} - 168 q^{36} - 114 q^{37} + 240 q^{38} - 54 q^{39} + 204 q^{42} + 228 q^{43} + 216 q^{44} + 196 q^{46} + 24 q^{47} - 22 q^{49} + 40 q^{50} - 60 q^{51} - 492 q^{52} - 152 q^{53} + 308 q^{56} - 12 q^{57} - 92 q^{58} - 324 q^{59} - 456 q^{61} - 54 q^{63} + 696 q^{64} - 120 q^{65} + 108 q^{66} + 166 q^{67} - 204 q^{68} - 300 q^{70} - 464 q^{71} + 12 q^{72} + 582 q^{73} + 104 q^{74} + 30 q^{75} - 44 q^{77} - 168 q^{78} - 98 q^{79} + 480 q^{80} - 90 q^{81} + 684 q^{82} - 60 q^{84} - 120 q^{85} + 308 q^{86} - 544 q^{88} + 96 q^{89} + 330 q^{91} + 168 q^{92} + 234 q^{93} + 60 q^{94} - 120 q^{95} - 432 q^{96} - 176 q^{98} + 240 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.3.n.a 105.n 7.d $8$ $2.861$ 8.0.\(\cdots\).16 None \(2\) \(-12\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
105.3.n.b 105.n 7.d $12$ $2.861$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(18\) \(0\) \(22\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{10})q^{2}+(2+\beta _{3})q^{3}+(4\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)