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 about

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

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

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

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