Properties

Label 105.4.m
Level $105$
Weight $4$
Character orbit 105.m
Rep. character $\chi_{105}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
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 104 48 56
Cusp forms 88 48 40
Eisenstein series 16 0 16

Trace form

\( 48 q + 4 q^{7} - 168 q^{8} + O(q^{10}) \) \( 48 q + 4 q^{7} - 168 q^{8} + 112 q^{11} + 168 q^{15} - 544 q^{16} - 96 q^{21} - 192 q^{22} + 400 q^{23} + 520 q^{25} + 1052 q^{28} - 48 q^{30} - 1344 q^{32} + 392 q^{35} - 1728 q^{36} - 456 q^{37} + 1068 q^{42} + 192 q^{43} - 208 q^{46} + 3528 q^{50} + 672 q^{51} - 1728 q^{53} - 48 q^{56} + 696 q^{57} + 3016 q^{58} + 840 q^{60} - 36 q^{63} - 4720 q^{65} - 4784 q^{67} + 2220 q^{70} - 3088 q^{71} - 1512 q^{72} + 2352 q^{77} + 1416 q^{78} - 3888 q^{81} - 472 q^{85} + 10832 q^{86} + 2128 q^{88} - 5664 q^{91} + 10600 q^{92} - 1368 q^{93} - 6912 q^{95} - 3888 q^{98} + O(q^{100}) \)

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.m.a 105.m 35.f $48$ $6.195$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{4}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)