Properties

Label 300.2.m
Level $300$
Weight $2$
Character orbit 300.m
Rep. character $\chi_{300}(61,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $16$
Newform subspaces $2$
Sturm bound $120$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 264 16 248
Cusp forms 216 16 200
Eisenstein series 48 0 48

Trace form

\( 16q - 4q^{9} + O(q^{10}) \) \( 16q - 4q^{9} + 6q^{11} + 10q^{17} + 10q^{19} + 4q^{21} + 10q^{25} + 24q^{29} - 6q^{31} + 10q^{33} + 10q^{35} - 10q^{37} + 30q^{41} - 80q^{43} - 40q^{47} - 16q^{49} - 16q^{51} - 30q^{53} - 10q^{55} - 36q^{59} + 32q^{61} + 10q^{63} - 10q^{65} + 20q^{67} + 4q^{69} - 40q^{71} - 20q^{73} + 40q^{77} + 8q^{79} - 4q^{81} + 10q^{83} - 20q^{85} - 20q^{87} - 30q^{89} + 30q^{91} - 40q^{93} - 20q^{95} + 20q^{97} - 4q^{99} + O(q^{100}) \)

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.m.a \(8\) \(2.396\) \(\Q(\zeta_{15})\) None \(0\) \(-2\) \(5\) \(-8\) \(q+\zeta_{15}^{5}q^{3}+(-1-2\zeta_{15}^{2}-\zeta_{15}^{3}+\cdots)q^{5}+\cdots\)
300.2.m.b \(8\) \(2.396\) 8.0.26265625.1 None \(0\) \(2\) \(-5\) \(8\) \(q+\beta _{3}q^{3}+(-1+\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)

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

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