Properties

Label 900.3.ba
Level $900$
Weight $3$
Character orbit 900.ba
Rep. character $\chi_{900}(161,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $80$
Newform subspaces $1$
Sturm bound $540$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.ba (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(540\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).

Total New Old
Modular forms 1488 80 1408
Cusp forms 1392 80 1312
Eisenstein series 96 0 96

Trace form

\( 80q + 16q^{7} + O(q^{10}) \) \( 80q + 16q^{7} - 8q^{13} + 60q^{19} - 120q^{25} + 120q^{31} + 116q^{37} - 80q^{43} + 440q^{49} + 120q^{55} + 80q^{61} + 24q^{67} + 128q^{73} + 40q^{79} + 40q^{85} - 140q^{91} + 384q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
900.3.ba.a \(80\) \(24.523\) None \(0\) \(0\) \(0\) \(16\)

Decomposition of \(S_{3}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)