Properties

Label 900.3.b
Level $900$
Weight $3$
Character orbit 900.b
Rep. character $\chi_{900}(449,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $540$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(540\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 396 12 384
Cusp forms 324 12 312
Eisenstein series 72 0 72

Trace form

\( 12q + O(q^{10}) \) \( 12q - 36q^{19} + 84q^{31} - 264q^{49} + 180q^{61} - 240q^{79} + 684q^{91} + O(q^{100}) \)

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.b.a \(4\) \(24.523\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{7}-\zeta_{8}^{2}q^{11}-7\zeta_{8}q^{13}+\zeta_{8}^{3}q^{17}+\cdots\)
900.3.b.b \(8\) \(24.523\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}-\beta _{3})q^{7}+(\beta _{2}+\beta _{5})q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)