Properties

Label 105.4.x
Level $105$
Weight $4$
Character orbit 105.x
Rep. character $\chi_{105}(2,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $176$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 208 208 0
Cusp forms 176 176 0
Eisenstein series 32 32 0

Trace form

\( 176q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 176q - 2q^{3} + 4q^{7} - 28q^{10} - 94q^{12} - 16q^{13} - 176q^{15} + 1016q^{16} + 14q^{18} - 148q^{21} - 32q^{22} - 76q^{25} - 32q^{27} + 776q^{28} - 500q^{30} - 296q^{31} - 430q^{33} - 880q^{36} + 212q^{37} - 1296q^{40} - 910q^{42} - 1360q^{43} + 490q^{45} + 1000q^{46} + 1604q^{48} - 268q^{51} + 68q^{52} + 1240q^{55} + 3548q^{57} - 1572q^{58} - 470q^{60} - 608q^{61} - 2974q^{63} - 92q^{66} - 1012q^{67} - 6720q^{70} + 866q^{72} + 2804q^{73} + 4086q^{75} - 8256q^{76} + 6888q^{78} - 2992q^{81} - 1112q^{82} + 4736q^{85} - 52q^{87} + 1284q^{88} - 5724q^{90} - 4192q^{91} + 3034q^{93} - 1824q^{96} + 7496q^{97} + O(q^{100}) \)

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.x.a \(176\) \(6.195\) None \(0\) \(-2\) \(0\) \(4\)