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Properties

Label 105.4.i
Level $105$
Weight $4$
Character orbit 105.i
Rep. character $\chi_{105}(16,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $5$
Sturm bound $64$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(64\)
Trace bound: \(2\)
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 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

Trace form

\( 32 q - 4 q^{2} - 12 q^{3} - 44 q^{4} + 44 q^{7} - 72 q^{8} - 144 q^{9} + O(q^{10}) \) \( 32 q - 4 q^{2} - 12 q^{3} - 44 q^{4} + 44 q^{7} - 72 q^{8} - 144 q^{9} - 40 q^{10} + 68 q^{11} - 144 q^{12} + 8 q^{13} + 136 q^{14} - 100 q^{16} + 8 q^{17} - 36 q^{18} - 136 q^{19} + 80 q^{20} - 168 q^{21} - 776 q^{22} + 328 q^{23} + 180 q^{24} - 400 q^{25} + 716 q^{26} + 216 q^{27} - 768 q^{28} + 1136 q^{29} + 92 q^{31} + 784 q^{32} - 264 q^{33} - 448 q^{34} + 220 q^{35} + 792 q^{36} - 660 q^{37} - 56 q^{38} - 588 q^{39} - 480 q^{40} - 1016 q^{41} + 564 q^{42} - 376 q^{43} + 368 q^{44} - 1180 q^{46} + 368 q^{47} + 2688 q^{48} + 252 q^{49} + 200 q^{50} + 48 q^{51} - 908 q^{52} + 2152 q^{53} + 1520 q^{55} + 588 q^{56} - 840 q^{57} + 2196 q^{58} + 1376 q^{59} + 2272 q^{61} - 6360 q^{62} - 36 q^{63} + 424 q^{64} - 420 q^{65} + 684 q^{66} - 228 q^{67} - 2988 q^{68} + 1296 q^{69} - 3020 q^{70} - 3008 q^{71} + 324 q^{72} - 972 q^{73} + 976 q^{74} - 300 q^{75} + 3944 q^{76} + 2560 q^{77} + 2472 q^{78} + 1076 q^{79} - 320 q^{80} - 1296 q^{81} + 332 q^{82} - 2288 q^{83} - 60 q^{84} + 1120 q^{85} - 6428 q^{86} - 2088 q^{87} + 232 q^{88} + 2072 q^{89} + 720 q^{90} + 2468 q^{91} - 5912 q^{92} + 420 q^{93} - 3292 q^{94} + 600 q^{95} + 1440 q^{96} - 1440 q^{97} - 3168 q^{98} - 1224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.i.a 105.i 7.c $2$ $6.195$ \(\Q(\sqrt{-3}) \) None \(-3\) \(3\) \(5\) \(-28\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
105.4.i.b 105.i 7.c $4$ $6.195$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(6\) \(10\) \(50\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-2\beta _{2}-\beta _{3})q^{2}+(3+3\beta _{2}+\cdots)q^{3}+\cdots\)
105.4.i.c 105.i 7.c $6$ $6.195$ 6.0.646154928.2 None \(-3\) \(9\) \(-15\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}+(3-3\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
105.4.i.d 105.i 7.c $10$ $6.195$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(-15\) \(-25\) \(-32\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{2}+(-3-3\beta _{4})q^{3}+(-5+\cdots)q^{4}+\cdots\)
105.4.i.e 105.i 7.c $10$ $6.195$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(1\) \(-15\) \(25\) \(56\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}-3\beta _{4}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)