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Properties

Label 2880.2.bl
Level $2880$
Weight $2$
Character orbit 2880.bl
Rep. character $\chi_{2880}(431,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $3$
Sturm bound $1152$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.bl (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(1152\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2880, [\chi])\).

Total New Old
Modular forms 1216 64 1152
Cusp forms 1088 64 1024
Eisenstein series 128 0 128

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + 16 q^{19} + 64 q^{49} + 32 q^{61} - 32 q^{67} + 32 q^{85} + 96 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2880, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2880.2.bl.a 2880.bl 48.k $8$ $22.997$ 8.0.3317760000.4 None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{5}+(-1+\beta _{6})q^{7}+(\beta _{3}-\beta _{5}+\cdots)q^{11}+\cdots\)
2880.2.bl.b 2880.bl 48.k $24$ $22.997$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$
2880.2.bl.c 2880.bl 48.k $32$ $22.997$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2880, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)