Properties

Label 900.3.u
Level $900$
Weight $3$
Character orbit 900.u
Rep. character $\chi_{900}(149,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $4$
Sturm bound $540$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(540\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 756 72 684
Cusp forms 684 72 612
Eisenstein series 72 0 72

Trace form

\( 72q - 14q^{9} + O(q^{10}) \) \( 72q - 14q^{9} + 36q^{11} - 8q^{21} - 72q^{29} - 30q^{31} + 8q^{39} + 72q^{41} + 204q^{49} - 198q^{51} - 18q^{59} - 96q^{61} + 396q^{69} - 108q^{79} + 158q^{81} + 168q^{91} - 606q^{99} + O(q^{100}) \)

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.u.a \(8\) \(24.523\) 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{5}-\beta _{7})q^{3}+(-3\beta _{1}-3\beta _{4}+\cdots)q^{7}+\cdots\)
900.3.u.b \(8\) \(24.523\) 8.0.12960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+3\beta _{1}q^{3}+(4\beta _{1}+\beta _{6})q^{7}-9\beta _{2}q^{9}+\cdots\)
900.3.u.c \(24\) \(24.523\) None \(0\) \(0\) \(0\) \(0\)
900.3.u.d \(32\) \(24.523\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)