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Properties

Label 300.3.u
Level $300$
Weight $3$
Character orbit 300.u
Rep. character $\chi_{300}(23,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $928$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.u (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(300, [\chi])\).

Total New Old
Modular forms 992 992 0
Cusp forms 928 928 0
Eisenstein series 64 64 0

Trace form

\( 928 q - 20 q^{4} - 6 q^{6} - 20 q^{9} + O(q^{10}) \) \( 928 q - 20 q^{4} - 6 q^{6} - 20 q^{9} - 8 q^{10} + 10 q^{12} - 32 q^{13} - 12 q^{16} + 14 q^{18} - 12 q^{21} + 56 q^{22} - 32 q^{25} + 64 q^{28} - 78 q^{30} + 20 q^{33} - 20 q^{34} - 70 q^{36} - 124 q^{40} + 454 q^{42} + 84 q^{45} - 12 q^{46} - 76 q^{48} - 324 q^{52} - 660 q^{54} + 52 q^{57} - 200 q^{58} - 826 q^{60} - 24 q^{61} - 20 q^{64} + 138 q^{66} - 20 q^{69} + 352 q^{70} + 590 q^{72} - 144 q^{73} + 96 q^{76} + 308 q^{78} - 12 q^{81} + 20 q^{82} - 10 q^{84} + 864 q^{85} - 760 q^{88} - 538 q^{90} - 388 q^{93} - 1420 q^{94} - 6 q^{96} + 288 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(300, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
300.3.u.a 300.u 300.u $928$ $8.174$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$