Properties

Label 300.3.k
Level $300$
Weight $3$
Character orbit 300.k
Rep. character $\chi_{300}(157,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $12$
Newform subspaces $3$
Sturm bound $180$
Trace bound $21$

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Defining parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(180\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 276 12 264
Cusp forms 204 12 192
Eisenstein series 72 0 72

Trace form

\( 12q - 20q^{7} + O(q^{10}) \) \( 12q - 20q^{7} + 32q^{11} + 40q^{17} - 12q^{21} + 40q^{23} + 108q^{31} - 60q^{33} + 80q^{41} - 120q^{43} + 48q^{51} + 200q^{53} - 120q^{57} - 356q^{61} - 60q^{63} + 40q^{67} + 160q^{71} + 20q^{73} + 200q^{77} - 108q^{81} + 240q^{83} - 60q^{87} + 180q^{91} - 120q^{93} - 300q^{97} + O(q^{100}) \)

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.k.a \(4\) \(8.174\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(-20\) \(q+\beta _{1}q^{3}+(-5+5\beta _{2}+2\beta _{3})q^{7}+3\beta _{2}q^{9}+\cdots\)
300.3.k.b \(4\) \(8.174\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+2\beta _{3}q^{7}+3\beta _{2}q^{9}+6q^{11}+\cdots\)
300.3.k.c \(4\) \(8.174\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-3\beta _{3}q^{7}+3\beta _{2}q^{9}+6q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)