Properties

Label 105.4.d
Level $105$
Weight $4$
Character orbit 105.d
Rep. character $\chi_{105}(64,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $64$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 52 16 36
Cusp forms 44 16 28
Eisenstein series 8 0 8

Trace form

\( 16 q - 60 q^{4} - 28 q^{5} - 12 q^{6} - 144 q^{9} + O(q^{10}) \) \( 16 q - 60 q^{4} - 28 q^{5} - 12 q^{6} - 144 q^{9} + 8 q^{10} - 24 q^{15} + 172 q^{16} - 72 q^{19} + 700 q^{20} - 84 q^{21} + 324 q^{24} - 8 q^{25} + 696 q^{26} - 1080 q^{29} - 432 q^{30} - 48 q^{31} - 152 q^{34} + 56 q^{35} + 540 q^{36} + 600 q^{39} - 2144 q^{40} + 1192 q^{41} + 32 q^{44} + 252 q^{45} - 64 q^{46} - 784 q^{49} - 1288 q^{50} - 1560 q^{51} + 108 q^{54} + 1408 q^{55} + 168 q^{56} + 352 q^{59} - 228 q^{60} - 440 q^{61} + 1476 q^{64} - 3312 q^{65} + 1920 q^{66} - 1776 q^{69} - 756 q^{70} + 904 q^{71} + 664 q^{74} + 528 q^{75} + 7840 q^{76} + 4880 q^{79} - 332 q^{80} + 1296 q^{81} + 1008 q^{84} - 1272 q^{85} - 4200 q^{86} + 3304 q^{89} - 72 q^{90} - 1456 q^{91} - 9304 q^{94} + 440 q^{95} + 1236 q^{96} + O(q^{100}) \)

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.d.a 105.d 5.b $6$ $6.195$ 6.0.84052224.1 None \(0\) \(0\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-3\beta _{3}q^{3}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
105.4.d.b 105.d 5.b $10$ $6.195$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}-3\beta _{2}q^{3}+(-5-\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)