Properties

Label 600.2.f
Level $600$
Weight $2$
Character orbit 600.f
Rep. character $\chi_{600}(49,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $5$
Sturm bound $240$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(240\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(600, [\chi])\).

Total New Old
Modular forms 144 10 134
Cusp forms 96 10 86
Eisenstein series 48 0 48

Trace form

\( 10q - 10q^{9} + O(q^{10}) \) \( 10q - 10q^{9} - 8q^{11} + 20q^{19} + 4q^{21} - 4q^{29} - 4q^{31} + 8q^{39} + 28q^{41} - 30q^{49} - 12q^{51} - 8q^{59} + 16q^{61} - 8q^{69} + 32q^{79} + 10q^{81} - 12q^{89} - 36q^{91} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
600.2.f.a \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+5iq^{7}-q^{9}-6q^{11}-3iq^{13}+\cdots\)
600.2.f.b \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}-4q^{11}+6iq^{13}+6iq^{17}+\cdots\)
600.2.f.c \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-4iq^{7}-q^{9}-6iq^{13}+2iq^{17}+\cdots\)
600.2.f.d \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-3iq^{7}-q^{9}+2q^{11}-3iq^{13}+\cdots\)
600.2.f.e \(2\) \(4.791\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}+4q^{11}+2iq^{13}+2iq^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)