Properties

Label 2800.2.e
Level $2800$
Weight $2$
Character orbit 2800.e
Rep. character $\chi_{2800}(2799,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $11$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 140 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(960\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\), \(19\)

Dimensions

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

Total New Old
Modular forms 516 72 444
Cusp forms 444 72 372
Eisenstein series 72 0 72

Trace form

\( 72 q - 72 q^{9} + O(q^{10}) \) \( 72 q - 72 q^{9} + 24 q^{21} + 48 q^{29} + 48 q^{49} + 72 q^{81} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2800.2.e.a 2800.e 140.c $4$ $22.358$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{12}q^{3}+(-2\zeta_{12}+\zeta_{12}^{3})q^{7}+\cdots\)
2800.2.e.b 2800.e 140.c $4$ $22.358$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{3}q^{3}+(-\zeta_{12}+\zeta_{12}^{3})q^{7}-q^{9}+\cdots\)
2800.2.e.c 2800.e 140.c $4$ $22.358$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{3}q^{3}+(-\zeta_{12}+\zeta_{12}^{3})q^{7}-q^{9}+\cdots\)
2800.2.e.d 2800.e 140.c $4$ $22.358$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)
2800.2.e.e 2800.e 140.c $8$ $22.358$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{24}+\zeta_{24}^{2})q^{3}+(-\zeta_{24}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
2800.2.e.f 2800.e 140.c $8$ $22.358$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{24}+\zeta_{24}^{2})q^{3}+(-\zeta_{24}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
2800.2.e.g 2800.e 140.c $8$ $22.358$ 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{3}-\beta _{6}q^{7}+(-1-\beta _{1})q^{9}+(\beta _{5}+\cdots)q^{11}+\cdots\)
2800.2.e.h 2800.e 140.c $8$ $22.358$ 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{3}+\beta _{6}q^{7}+(-1-\beta _{1})q^{9}+(\beta _{5}+\cdots)q^{11}+\cdots\)
2800.2.e.i 2800.e 140.c $8$ $22.358$ 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{6})q^{7}+\beta _{4}q^{9}+\cdots\)
2800.2.e.j 2800.e 140.c $8$ $22.358$ 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}+(\beta _{3}-\beta _{5})q^{7}+(-1-\beta _{6}+\cdots)q^{9}+\cdots\)
2800.2.e.k 2800.e 140.c $8$ $22.358$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\beta _{3}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 3}\)