Properties

Label 300.2.h
Level $300$
Weight $2$
Character orbit 300.h
Rep. character $\chi_{300}(299,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $3$
Sturm bound $120$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

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

Total New Old
Modular forms 72 40 32
Cusp forms 48 32 16
Eisenstein series 24 8 16

Trace form

\( 32q + 8q^{4} - 6q^{6} + 4q^{9} + O(q^{10}) \) \( 32q + 8q^{4} - 6q^{6} + 4q^{9} - 8q^{16} + 16q^{21} - 22q^{24} - 52q^{34} - 6q^{36} - 16q^{46} + 8q^{49} + 76q^{54} - 56q^{61} + 80q^{64} - 22q^{66} - 36q^{76} - 60q^{81} - 112q^{84} - 48q^{94} + 6q^{96} + O(q^{100}) \)

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.h.a \(8\) \(2.396\) 8.0.342102016.5 None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
300.2.h.b \(8\) \(2.396\) 8.0.342102016.5 None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
300.2.h.c \(16\) \(2.396\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{10}q^{3}-\beta _{4}q^{4}-\beta _{12}q^{6}+\cdots\)

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

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