Properties

Label 1440.2.bi
Level $1440$
Weight $2$
Character orbit 1440.bi
Rep. character $\chi_{1440}(847,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $5$
Sturm bound $576$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.bi (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 5 \)
Sturm bound: \(576\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1440, [\chi])\).

Total New Old
Modular forms 640 64 576
Cusp forms 512 56 456
Eisenstein series 128 8 120

Trace form

\( 56 q + O(q^{10}) \) \( 56 q - 8 q^{11} - 28 q^{35} + 8 q^{41} + 36 q^{43} + 8 q^{65} + 28 q^{67} + 16 q^{73} + 36 q^{83} + 40 q^{91} - 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1440, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1440.2.bi.a $4$ $11.498$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-4\) \(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-1+\zeta_{8}^{2})q^{7}+\cdots\)
1440.2.bi.b $4$ $11.498$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(4\) \(q+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+(1-\zeta_{8}^{2})q^{7}+\cdots\)
1440.2.bi.c $8$ $11.498$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{20}^{4}-\zeta_{20}^{5}-\zeta_{20}^{6}+\zeta_{20}^{7})q^{5}+\cdots\)
1440.2.bi.d $16$ $11.498$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{5}-\beta _{10}q^{7}-\beta _{15}q^{11}+\beta _{7}q^{13}+\cdots\)
1440.2.bi.e $24$ $11.498$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1440, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)