Properties

Label 300.2.d
Level $300$
Weight $2$
Character orbit 300.d
Rep. character $\chi_{300}(49,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 78 2 76
Cusp forms 42 2 40
Eisenstein series 36 0 36

Trace form

\( 2q - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{9} + 12q^{11} - 10q^{19} - 2q^{21} + 12q^{29} - 2q^{31} - 10q^{39} + 12q^{49} - 12q^{51} + 12q^{59} - 26q^{61} + 12q^{69} - 16q^{79} + 2q^{81} - 10q^{91} - 12q^{99} + O(q^{100}) \)

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.d.a \(2\) \(2.396\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}-q^{9}+6q^{11}+5iq^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)