Properties

Label 2240.2.g
Level $2240$
Weight $2$
Character orbit 2240.g
Rep. character $\chi_{2240}(449,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $16$
Sturm bound $768$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(768\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2240, [\chi])\).

Total New Old
Modular forms 408 72 336
Cusp forms 360 72 288
Eisenstein series 48 0 48

Trace form

\( 72 q - 72 q^{9} + O(q^{10}) \) \( 72 q - 72 q^{9} - 8 q^{25} + 16 q^{41} - 48 q^{45} - 72 q^{49} - 32 q^{61} - 16 q^{65} + 128 q^{69} + 72 q^{81} + 16 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2240, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2240.2.g.a $2$ $17.886$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2+i)q^{5}-iq^{7}+2q^{9}+\cdots\)
2240.2.g.b $2$ $17.886$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2-i)q^{5}-iq^{7}+2q^{9}+\cdots\)
2240.2.g.c $2$ $17.886$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+2i)q^{5}+iq^{7}+3q^{9}-4iq^{13}+\cdots\)
2240.2.g.d $2$ $17.886$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1+2i)q^{5}-iq^{7}+3q^{9}-4iq^{13}+\cdots\)
2240.2.g.e $2$ $17.886$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+3iq^{3}+(2+i)q^{5}+iq^{7}-6q^{9}+\cdots\)
2240.2.g.f $2$ $17.886$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+3iq^{3}+(2-i)q^{5}+iq^{7}-6q^{9}+\cdots\)
2240.2.g.g $2$ $17.886$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+(2-i)q^{5}-iq^{7}+2q^{9}-3q^{11}+\cdots\)
2240.2.g.h $2$ $17.886$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+(2+i)q^{5}-iq^{7}+2q^{9}+3q^{11}+\cdots\)
2240.2.g.i $4$ $17.886$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
2240.2.g.j $4$ $17.886$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots\)
2240.2.g.k $4$ $17.886$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}+2q^{9}+\beta _{3}q^{11}+\cdots\)
2240.2.g.l $6$ $17.886$ 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{5})q^{5}-\beta _{4}q^{7}+\cdots\)
2240.2.g.m $6$ $17.886$ 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+(-\beta _{1}+\beta _{5})q^{5}-\beta _{4}q^{7}+\cdots\)
2240.2.g.n $10$ $17.886$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{1}q^{3}-\beta _{4}q^{5}-\beta _{5}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
2240.2.g.o $10$ $17.886$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{5}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
2240.2.g.p $12$ $17.886$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{3}-\beta _{10}q^{5}-\beta _{5}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)