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Properties

Label 20.7.d
Level $20$
Weight $7$
Character orbit 20.d
Rep. character $\chi_{20}(19,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $4$
Sturm bound $21$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 20.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(21\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(20, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 16 16 0
Eisenstein series 4 4 0

Trace form

\( 16 q + 64 q^{4} - 24 q^{5} + 32 q^{6} + 2912 q^{9} + O(q^{10}) \) \( 16 q + 64 q^{4} - 24 q^{5} + 32 q^{6} + 2912 q^{9} + 1296 q^{10} - 7872 q^{14} - 4544 q^{16} - 14784 q^{20} + 5104 q^{21} + 24128 q^{24} - 944 q^{25} - 12000 q^{26} + 9888 q^{29} - 4480 q^{30} + 100800 q^{34} + 102848 q^{36} + 8256 q^{40} - 170928 q^{41} - 165120 q^{44} - 188344 q^{45} - 295168 q^{46} + 224352 q^{49} + 128736 q^{50} + 217856 q^{54} + 541632 q^{56} - 902400 q^{60} + 650192 q^{61} - 6656 q^{64} + 564672 q^{65} - 1403520 q^{66} - 335504 q^{69} + 1578080 q^{70} + 335520 q^{74} + 2515200 q^{76} - 2109504 q^{80} - 1173760 q^{81} - 2526464 q^{84} - 905088 q^{85} - 4990368 q^{86} - 566112 q^{89} + 4095216 q^{90} + 3869888 q^{94} + 10556672 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
20.7.d.a 20.d 20.d $1$ $4.601$ \(\Q\) \(\Q(\sqrt{-5}) \) \(-8\) \(-44\) \(-125\) \(524\) $\mathrm{U}(1)[D_{2}]$ \(q-8q^{2}-44q^{3}+2^{6}q^{4}-5^{3}q^{5}+352q^{6}+\cdots\)
20.7.d.b 20.d 20.d $1$ $4.601$ \(\Q\) \(\Q(\sqrt{-5}) \) \(8\) \(44\) \(-125\) \(-524\) $\mathrm{U}(1)[D_{2}]$ \(q+8q^{2}+44q^{3}+2^{6}q^{4}-5^{3}q^{5}+352q^{6}+\cdots\)
20.7.d.c 20.d 20.d $2$ $4.601$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-234\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2iq^{2}-2^{6}q^{4}+(-117+11i)q^{5}+\cdots\)
20.7.d.d 20.d 20.d $12$ $4.601$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(460\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(6+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)