Properties

Label 300.2.j
Level $300$
Weight $2$
Character orbit 300.j
Rep. character $\chi_{300}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $36$
Newform subspaces $4$
Sturm bound $120$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(7\), \(19\)

Dimensions

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

Total New Old
Modular forms 144 36 108
Cusp forms 96 36 60
Eisenstein series 48 0 48

Trace form

\( 36q + 8q^{6} + 12q^{8} + O(q^{10}) \) \( 36q + 8q^{6} + 12q^{8} + 8q^{12} + 4q^{13} - 24q^{16} + 20q^{17} - 12q^{22} - 32q^{26} + 4q^{28} - 20q^{32} - 8q^{33} - 8q^{36} - 4q^{37} - 16q^{38} - 32q^{41} - 20q^{42} - 40q^{46} - 16q^{48} + 8q^{52} - 4q^{53} + 8q^{56} + 20q^{58} + 64q^{61} + 56q^{62} + 48q^{66} + 16q^{68} + 12q^{72} - 44q^{73} - 16q^{76} - 48q^{77} + 24q^{78} - 36q^{81} - 16q^{82} - 8q^{86} - 60q^{88} - 56q^{92} + 16q^{93} + 32q^{96} + 20q^{97} - 24q^{98} + O(q^{100}) \)

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.j.a \(8\) \(2.396\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{5})q^{2}+\zeta_{24}q^{3}+\cdots\)
300.2.j.b \(8\) \(2.396\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{4}+\cdots\)
300.2.j.c \(8\) \(2.396\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}-\zeta_{24}^{5}q^{3}+(\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
300.2.j.d \(12\) \(2.396\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{2}+\beta _{8}+\beta _{9})q^{4}+\cdots\)

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

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