Properties

Label 440.2.b
Level $440$
Weight $2$
Character orbit 440.b
Rep. character $\chi_{440}(89,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $4$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 440.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(440, [\chi])\).

Total New Old
Modular forms 80 14 66
Cusp forms 64 14 50
Eisenstein series 16 0 16

Trace form

\( 14 q + 4 q^{5} - 14 q^{9} + O(q^{10}) \) \( 14 q + 4 q^{5} - 14 q^{9} + 6 q^{11} - 14 q^{15} - 8 q^{21} - 8 q^{25} - 4 q^{29} + 4 q^{35} + 16 q^{39} + 20 q^{41} - 14 q^{45} - 18 q^{49} - 24 q^{51} - 20 q^{59} + 52 q^{61} - 32 q^{65} + 12 q^{69} + 8 q^{71} + 50 q^{75} + 40 q^{79} + 46 q^{81} - 20 q^{85} + 20 q^{89} - 40 q^{91} + 24 q^{95} - 18 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(440, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
440.2.b.a $2$ $3.513$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}+(-1+i)q^{5}+iq^{7}-q^{9}+\cdots\)
440.2.b.b $2$ $3.513$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1-i)q^{5}-2iq^{7}-q^{9}+q^{11}+\cdots\)
440.2.b.c $2$ $3.513$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+(2+i)q^{5}+iq^{7}+2q^{9}-q^{11}+\cdots\)
440.2.b.d $8$ $3.513$ 8.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(440, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 2}\)