Properties

Label 105.3.r
Level $105$
Weight $3$
Character orbit 105.r
Rep. character $\chi_{105}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 72 32 40
Cusp forms 56 32 24
Eisenstein series 16 0 16

Trace form

\( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9} + O(q^{10}) \) \( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9} + 78 q^{10} - 28 q^{11} + 60 q^{14} - 24 q^{15} - 40 q^{16} - 60 q^{19} + 12 q^{21} - 34 q^{25} - 96 q^{26} - 88 q^{29} + 84 q^{31} - 170 q^{35} - 192 q^{36} + 36 q^{39} + 330 q^{40} + 320 q^{44} + 18 q^{45} - 60 q^{46} + 356 q^{49} + 12 q^{51} - 468 q^{56} - 804 q^{59} - 198 q^{60} + 336 q^{61} - 400 q^{64} - 46 q^{65} - 108 q^{66} - 438 q^{70} + 344 q^{71} + 900 q^{74} + 144 q^{75} - 20 q^{79} + 1140 q^{80} - 144 q^{81} + 780 q^{84} + 304 q^{85} + 144 q^{86} + 24 q^{89} - 224 q^{91} - 924 q^{94} - 342 q^{95} + 900 q^{96} + 168 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.3.r.a $32$ $2.861$ None \(0\) \(0\) \(-6\) \(0\)

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

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