Properties

Label 840.2.t
Level $840$
Weight $2$
Character orbit 840.t
Rep. character $\chi_{840}(169,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $5$
Sturm bound $384$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 840.t (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(384\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(840, [\chi])\).

Total New Old
Modular forms 208 20 188
Cusp forms 176 20 156
Eisenstein series 32 0 32

Trace form

\( 20 q - 8 q^{5} - 20 q^{9} + O(q^{10}) \) \( 20 q - 8 q^{5} - 20 q^{9} + 4 q^{21} + 4 q^{25} + 32 q^{29} - 8 q^{31} + 8 q^{39} - 32 q^{41} + 8 q^{45} - 20 q^{49} - 24 q^{51} + 8 q^{55} - 32 q^{61} + 24 q^{71} + 16 q^{79} + 20 q^{81} - 16 q^{85} + 48 q^{89} - 24 q^{91} + 8 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(840, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
840.2.t.a $2$ $6.707$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{3}+(-1-2i)q^{5}-iq^{7}-q^{9}+\cdots\)
840.2.t.b $2$ $6.707$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{3}+(-1+2i)q^{5}-iq^{7}-q^{9}+\cdots\)
840.2.t.c $4$ $6.707$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{1}q^{7}-q^{9}-2q^{11}+\cdots\)
840.2.t.d $6$ $6.707$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}-q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
840.2.t.e $6$ $6.707$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)