Properties

Label 2800.2.g
Level $2800$
Weight $2$
Character orbit 2800.g
Rep. character $\chi_{2800}(449,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $22$
Sturm bound $960$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2800.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(960\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2800, [\chi])\).

Total New Old
Modular forms 516 54 462
Cusp forms 444 54 390
Eisenstein series 72 0 72

Trace form

\( 54q - 54q^{9} + O(q^{10}) \) \( 54q - 54q^{9} + 12q^{11} - 16q^{19} + 4q^{29} + 16q^{31} + 40q^{39} + 4q^{41} - 54q^{49} + 16q^{51} - 52q^{61} + 32q^{69} - 52q^{71} + 4q^{79} + 38q^{81} - 20q^{89} + 12q^{91} - 76q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2800, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2800.2.g.a \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}-iq^{7}-6q^{9}+5q^{11}-6iq^{13}+\cdots\)
2800.2.g.b \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}+iq^{7}-6q^{9}+5q^{11}-5iq^{13}+\cdots\)
2800.2.g.c \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}+iq^{7}-6q^{9}+5q^{11}+3iq^{13}+\cdots\)
2800.2.g.d \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}-iq^{7}-q^{9}-5q^{11}+8iq^{17}+\cdots\)
2800.2.g.e \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}+iq^{7}-q^{9}-3q^{11}-4iq^{13}+\cdots\)
2800.2.g.f \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}+iq^{7}-q^{9}-q^{11}-4iq^{13}+\cdots\)
2800.2.g.g \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}-iq^{7}-q^{9}-2iq^{17}-2q^{19}+\cdots\)
2800.2.g.h \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}+iq^{7}-q^{9}-4iq^{13}-6iq^{17}+\cdots\)
2800.2.g.i \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}+2q^{9}-3q^{11}-2iq^{13}+\cdots\)
2800.2.g.j \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}+2q^{9}-3q^{11}+iq^{13}+\cdots\)
2800.2.g.k \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}+2q^{9}+q^{11}+6iq^{13}+\cdots\)
2800.2.g.l \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}+2q^{9}+3q^{11}-5iq^{13}+\cdots\)
2800.2.g.m \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}+2q^{9}+5q^{11}+iq^{13}+\cdots\)
2800.2.g.n \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+3q^{9}-4q^{11}+6iq^{13}+2iq^{17}+\cdots\)
2800.2.g.o \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+3q^{9}-q^{11}-2iq^{13}+4iq^{17}+\cdots\)
2800.2.g.p \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+3q^{9}+4q^{11}-2iq^{13}-6iq^{17}+\cdots\)
2800.2.g.q \(2\) \(22.358\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}+3q^{9}+5q^{11}+6iq^{13}+4iq^{17}+\cdots\)
2800.2.g.r \(4\) \(22.358\) \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-6+\beta _{3})q^{9}+(-3+\cdots)q^{11}+\cdots\)
2800.2.g.s \(4\) \(22.358\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{3}-\beta _{1}q^{7}+(-3+2\beta _{3})q^{9}+\cdots\)
2800.2.g.t \(4\) \(22.358\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
2800.2.g.u \(4\) \(22.358\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots\)
2800.2.g.v \(4\) \(22.358\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1400, [\chi])\)\(^{\oplus 2}\)