Properties

Label 105.4.s
Level $105$
Weight $4$
Character orbit 105.s
Rep. character $\chi_{105}(26,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $2$
Sturm bound $64$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(105, [\chi])\).

Total New Old
Modular forms 104 64 40
Cusp forms 88 64 24
Eisenstein series 16 0 16

Trace form

\( 64 q + 128 q^{4} + 92 q^{7} + 2 q^{9} + O(q^{10}) \) \( 64 q + 128 q^{4} + 92 q^{7} + 2 q^{9} + 330 q^{12} + 40 q^{15} - 752 q^{16} - 182 q^{18} - 396 q^{19} - 474 q^{21} + 408 q^{22} - 144 q^{24} - 800 q^{25} + 700 q^{28} + 140 q^{30} + 1020 q^{31} + 744 q^{33} - 1224 q^{36} - 1316 q^{37} - 72 q^{39} + 102 q^{42} + 664 q^{43} - 990 q^{45} - 936 q^{46} + 1960 q^{49} + 1860 q^{51} + 6756 q^{52} + 6036 q^{54} - 1632 q^{57} - 2160 q^{58} + 810 q^{60} - 3324 q^{61} - 1432 q^{63} - 3904 q^{64} - 5700 q^{66} - 2596 q^{67} - 900 q^{70} + 4970 q^{72} + 756 q^{73} - 3792 q^{78} - 652 q^{79} - 1534 q^{81} - 5832 q^{82} - 9300 q^{84} + 1440 q^{85} - 6756 q^{87} + 3336 q^{88} + 4164 q^{91} - 864 q^{93} - 2304 q^{94} + 11412 q^{96} + 6256 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.4.s.a 105.s 21.g $32$ $6.195$ None \(0\) \(-2\) \(-80\) \(46\) $\mathrm{SU}(2)[C_{6}]$
105.4.s.b 105.s 21.g $32$ $6.195$ None \(0\) \(2\) \(80\) \(46\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)