Properties

Label 300.3.b
Level $300$
Weight $3$
Character orbit 300.b
Rep. character $\chi_{300}(149,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $180$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(180\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 138 12 126
Cusp forms 102 12 90
Eisenstein series 36 0 36

Trace form

\( 12q + 2q^{9} + O(q^{10}) \) \( 12q + 2q^{9} + 18q^{19} + 98q^{21} - 102q^{31} - 62q^{39} - 30q^{49} + 330q^{51} - 342q^{61} + 60q^{69} + 384q^{79} + 262q^{81} - 558q^{91} - 270q^{99} + O(q^{100}) \)

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.b.a \(2\) \(8.174\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}+2iq^{7}-9q^{9}+22iq^{13}+\cdots\)
300.3.b.b \(2\) \(8.174\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}-13iq^{7}-9q^{9}-23iq^{13}+\cdots\)
300.3.b.c \(4\) \(8.174\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{3}+\beta _{1}q^{7}+(1-2\beta _{2}+\cdots)q^{9}+\cdots\)
300.3.b.d \(4\) \(8.174\) \(\Q(i, \sqrt{35})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-8\beta _{2}q^{7}+(9+\beta _{3})q^{9}+(-3+\cdots)q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)