Properties

Label 300.2.e
Level $300$
Weight $2$
Character orbit 300.e
Rep. character $\chi_{300}(251,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $5$
Sturm bound $120$
Trace bound $12$

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Defining parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(120\)
Trace bound: \(12\)
Distinguishing \(T_p\): \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(300, [\chi])\).

Total New Old
Modular forms 72 44 28
Cusp forms 48 32 16
Eisenstein series 24 12 12

Trace form

\( 32q + 2q^{6} + 4q^{9} + O(q^{10}) \) \( 32q + 2q^{6} + 4q^{9} - 4q^{12} + 8q^{13} + 8q^{16} - 16q^{18} - 8q^{21} + 4q^{22} - 2q^{24} - 28q^{28} + 16q^{33} + 28q^{34} - 46q^{36} - 8q^{37} + 12q^{42} - 40q^{46} + 36q^{48} - 8q^{49} + 32q^{52} - 20q^{54} - 24q^{57} + 36q^{58} - 24q^{61} - 24q^{64} + 18q^{66} - 40q^{69} - 24q^{72} + 60q^{76} - 40q^{78} - 28q^{81} - 40q^{82} + 56q^{84} - 44q^{88} - 32q^{93} - 56q^{94} - 58q^{96} + 48q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(300, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
300.2.e.a \(4\) \(2.396\) \(\Q(\sqrt{3}, \sqrt{-5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots\)
300.2.e.b \(4\) \(2.396\) \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.2.e.c \(8\) \(2.396\) 8.0.342102016.5 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
300.2.e.d \(8\) \(2.396\) 8.0.4521217600.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
300.2.e.e \(8\) \(2.396\) 8.0.4521217600.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+\beta _{3}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(300, [\chi])\) into lower level spaces

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