Properties

Label 1200.2.f
Level $1200$
Weight $2$
Character orbit 1200.f
Rep. character $\chi_{1200}(49,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $9$
Sturm bound $480$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1200.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(480\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1200, [\chi])\).

Total New Old
Modular forms 276 18 258
Cusp forms 204 18 186
Eisenstein series 72 0 72

Trace form

\( 18q - 18q^{9} + O(q^{10}) \) \( 18q - 18q^{9} - 20q^{19} + 4q^{29} - 4q^{31} + 8q^{39} + 20q^{41} - 26q^{49} + 20q^{51} - 32q^{59} - 20q^{61} + 16q^{69} + 32q^{71} + 18q^{81} - 36q^{89} + 68q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1200.2.f.a \(2\) \(9.582\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}-q^{9}-6q^{11}-5iq^{13}+\cdots\)
1200.2.f.b \(2\) \(9.582\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{9}-4q^{11}+2iq^{13}+2iq^{17}+\cdots\)
1200.2.f.c \(2\) \(9.582\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+3iq^{7}-q^{9}-2q^{11}-3iq^{13}+\cdots\)
1200.2.f.d \(2\) \(9.582\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+3iq^{7}-q^{9}-2q^{11}-iq^{13}+\cdots\)
1200.2.f.e \(2\) \(9.582\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+4iq^{7}-q^{9}-2iq^{13}+6iq^{17}+\cdots\)
1200.2.f.f \(2\) \(9.582\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+4iq^{7}-q^{9}-6iq^{13}+2iq^{17}+\cdots\)
1200.2.f.g \(2\) \(9.582\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}+4q^{11}-6iq^{13}-6iq^{17}+\cdots\)
1200.2.f.h \(2\) \(9.582\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}+4q^{11}-2iq^{13}-2iq^{17}+\cdots\)
1200.2.f.i \(2\) \(9.582\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+5iq^{7}-q^{9}+6q^{11}+3iq^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)