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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.4.s.a \(32\) \(6.195\) None \(0\) \(-2\) \(-80\) \(46\)
105.4.s.b \(32\) \(6.195\) None \(0\) \(2\) \(80\) \(46\)

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

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