Properties

Label 70.4.c
Level $70$
Weight $4$
Character orbit 70.c
Rep. character $\chi_{70}(29,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 70.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(70, [\chi])\).

Total New Old
Modular forms 40 8 32
Cusp forms 32 8 24
Eisenstein series 8 0 8

Trace form

\( 8 q - 32 q^{4} + 4 q^{5} - 196 q^{9} + O(q^{10}) \) \( 8 q - 32 q^{4} + 4 q^{5} - 196 q^{9} - 56 q^{10} - 36 q^{11} + 56 q^{14} + 40 q^{15} + 128 q^{16} - 96 q^{19} - 16 q^{20} - 196 q^{21} + 636 q^{25} + 368 q^{26} + 316 q^{29} - 200 q^{30} + 72 q^{31} - 784 q^{34} + 56 q^{35} + 784 q^{36} - 884 q^{39} + 224 q^{40} + 400 q^{41} + 144 q^{44} + 1548 q^{45} - 80 q^{46} - 392 q^{49} + 456 q^{50} - 812 q^{51} - 2016 q^{54} + 896 q^{55} - 224 q^{56} - 1176 q^{59} - 160 q^{60} - 1176 q^{61} - 512 q^{64} + 1096 q^{65} + 416 q^{66} - 5480 q^{69} - 504 q^{70} + 2360 q^{71} + 1808 q^{74} - 3360 q^{75} + 384 q^{76} + 404 q^{79} + 64 q^{80} + 3136 q^{81} + 784 q^{84} - 492 q^{85} - 2368 q^{86} + 2536 q^{89} + 3048 q^{90} + 140 q^{91} + 832 q^{94} + 2260 q^{95} + 8184 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(70, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
70.4.c.a 70.c 5.b $2$ $4.130$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+7iq^{3}-4q^{4}+(10+5i)q^{5}+\cdots\)
70.4.c.b 70.c 5.b $6$ $4.130$ 6.0.\(\cdots\).1 None \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{3}q^{2}+(-2\beta _{3}+\beta _{5})q^{3}-4q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(70, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(70, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)