Properties

Label 300.3.f
Level $300$
Weight $3$
Character orbit 300.f
Rep. character $\chi_{300}(199,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $3$
Sturm bound $180$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(180\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 132 36 96
Cusp forms 108 36 72
Eisenstein series 24 0 24

Trace form

\( 36q + 4q^{4} - 12q^{6} + 108q^{9} + O(q^{10}) \) \( 36q + 4q^{4} - 12q^{6} + 108q^{9} + 44q^{14} + 116q^{16} + 36q^{24} - 212q^{26} + 40q^{29} - 24q^{34} + 12q^{36} + 168q^{41} - 328q^{44} - 40q^{46} + 76q^{49} - 36q^{54} - 112q^{56} + 24q^{61} - 68q^{64} + 48q^{66} + 192q^{69} + 56q^{74} - 96q^{76} + 324q^{81} + 456q^{84} - 308q^{86} - 744q^{89} - 312q^{94} - 348q^{96} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
300.3.f.a \(4\) \(8.174\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
300.3.f.b \(16\) \(8.174\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{12}q^{2}-\beta _{9}q^{3}+(-1+\beta _{4})q^{4}+\cdots\)
300.3.f.c \(16\) \(8.174\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)