Properties

Label 900.3.g
Level $900$
Weight $3$
Character orbit 900.g
Rep. character $\chi_{900}(701,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $540$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(540\)
Trace bound: \(7\)
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

\( 12q + 16q^{7} + O(q^{10}) \) \( 12q + 16q^{7} - 8q^{13} - 44q^{19} - 76q^{31} + 136q^{37} - 80q^{43} + 24q^{49} - 60q^{61} + 304q^{67} - 152q^{73} - 80q^{79} - 196q^{91} + 424q^{97} + O(q^{100}) \)

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.g.a \(2\) \(24.523\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+\beta q^{11}-7q^{13}-\beta q^{17}-7q^{19}+\cdots\)
900.3.g.b \(2\) \(24.523\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(2\) \(q+q^{7}+\beta q^{11}+7q^{13}+\beta q^{17}-7q^{19}+\cdots\)
900.3.g.c \(4\) \(24.523\) \(\Q(\sqrt{-2}, \sqrt{-23})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{7}-7\beta _{1}q^{11}+3\beta _{2}q^{13}-2\beta _{3}q^{17}+\cdots\)
900.3.g.d \(4\) \(24.523\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(16\) \(q+(4-\beta _{2})q^{7}+(-\beta _{1}+\beta _{3})q^{11}+(-2+\cdots)q^{13}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)