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Properties

Label 300.3.c
Level $300$
Weight $3$
Character orbit 300.c
Rep. character $\chi_{300}(151,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $7$
Sturm bound $180$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 300.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(180\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(13\)

Dimensions

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

Total New Old
Modular forms 132 38 94
Cusp forms 108 38 70
Eisenstein series 24 0 24

Trace form

\( 38q - 2q^{2} - 8q^{4} - 6q^{6} + 4q^{8} - 114q^{9} + O(q^{10}) \) \( 38q - 2q^{2} - 8q^{4} - 6q^{6} + 4q^{8} - 114q^{9} + 12q^{12} - 20q^{13} + 52q^{14} + 20q^{16} - 20q^{17} + 6q^{18} + 24q^{21} - 92q^{22} - 36q^{24} - 16q^{26} - 76q^{28} - 12q^{29} + 108q^{32} + 24q^{33} + 164q^{34} + 24q^{36} + 60q^{37} - 32q^{38} - 116q^{41} - 84q^{42} + 64q^{46} - 96q^{48} - 234q^{49} + 136q^{52} - 204q^{53} + 18q^{54} - 472q^{56} - 72q^{57} + 152q^{58} + 156q^{61} + 32q^{62} + 316q^{64} - 168q^{66} + 224q^{68} - 96q^{69} - 12q^{72} + 332q^{73} + 332q^{74} + 240q^{76} + 192q^{77} + 228q^{78} + 342q^{81} + 76q^{82} - 24q^{84} - 76q^{86} - 140q^{88} - 132q^{89} - 336q^{92} - 120q^{93} - 208q^{94} + 156q^{96} - 436q^{97} - 658q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.c.a \(2\) \(8.174\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
300.3.c.b \(2\) \(8.174\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
300.3.c.c \(2\) \(8.174\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
300.3.c.d \(8\) \(8.174\) 8.0.85100625.1 None \(-4\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+\beta _{6}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.e \(8\) \(8.174\) 8.0.4069419264.1 None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}-\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.f \(8\) \(8.174\) 8.0.6080256576.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}-\beta _{2}q^{3}+(1-\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.g \(8\) \(8.174\) 8.0.4069419264.1 None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)