Properties

Label 300.2.i
Level $300$
Weight $2$
Character orbit 300.i
Rep. character $\chi_{300}(257,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $3$
Sturm bound $120$
Trace bound $21$

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Defining parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 156 12 144
Cusp forms 84 12 72
Eisenstein series 72 0 72

Trace form

\( 12q - 2q^{3} + 4q^{7} + O(q^{10}) \) \( 12q - 2q^{3} + 4q^{7} + 12q^{13} + 8q^{21} - 14q^{27} - 12q^{31} - 20q^{33} + 12q^{37} + 12q^{43} - 20q^{51} + 4q^{57} + 28q^{61} - 8q^{63} + 4q^{67} - 4q^{73} - 68q^{81} - 20q^{87} - 108q^{91} - 8q^{93} - 36q^{97} + O(q^{100}) \)

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.i.a \(4\) \(2.396\) \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(0\) \(4\) \(q+(-1+\beta _{3})q^{3}+(1-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
300.2.i.b \(4\) \(2.396\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+2\beta _{3}q^{7}+3\beta _{2}q^{9}+4\beta _{1}q^{13}+\cdots\)
300.2.i.c \(4\) \(2.396\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-3\beta _{3}q^{7}+3\beta _{2}q^{9}-\beta _{1}q^{13}+\cdots\)

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

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