Properties

Label 1440.2.o
Level $1440$
Weight $2$
Character orbit 1440.o
Rep. character $\chi_{1440}(1439,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $576$
Trace bound $43$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 60 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(43\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 320 24 296
Cusp forms 256 24 232
Eisenstein series 64 0 64

Trace form

\( 24q + O(q^{10}) \) \( 24q - 16q^{25} - 8q^{49} - 16q^{61} + 40q^{85} + O(q^{100}) \)

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.o.a \(12\) \(11.498\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+\beta _{9}q^{7}+(-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)
1440.2.o.b \(12\) \(11.498\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}-\beta _{9}q^{7}+(\beta _{2}-\beta _{3}-\beta _{4})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)