Properties

Label 300.3.s
Level $300$
Weight $3$
Character orbit 300.s
Rep. character $\chi_{300}(41,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $80$
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.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{10})\)
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 504 80 424
Cusp forms 456 80 376
Eisenstein series 48 0 48

Trace form

\( 80 q + 2 q^{3} - 8 q^{7} - 10 q^{9} + O(q^{10}) \) \( 80 q + 2 q^{3} - 8 q^{7} - 10 q^{9} + 28 q^{13} - 30 q^{15} - 30 q^{19} - 30 q^{21} + 60 q^{25} - 7 q^{27} - 85 q^{33} - 124 q^{37} + 70 q^{39} + 28 q^{43} - 40 q^{45} + 680 q^{49} - 170 q^{51} - 60 q^{55} - 348 q^{57} + 20 q^{61} - 37 q^{63} + 222 q^{67} + 50 q^{69} + 164 q^{73} - 115 q^{75} + 220 q^{79} + 110 q^{81} + 520 q^{85} - 245 q^{87} + 70 q^{91} - 522 q^{93} - 228 q^{97} - 390 q^{99} + O(q^{100}) \)

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.s.a 300.s 75.j $80$ $8.174$ None \(0\) \(2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(300, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)