Properties

Label 900.3.p
Level $900$
Weight $3$
Character orbit 900.p
Rep. character $\chi_{900}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $6$
Sturm bound $540$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(540\)
Trace bound: \(3\)
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 76 680
Cusp forms 684 76 608
Eisenstein series 72 0 72

Trace form

\( 76q + q^{3} - q^{7} + 19q^{9} + O(q^{10}) \) \( 76q + q^{3} - q^{7} + 19q^{9} + 5q^{13} + 2q^{19} - 29q^{21} - 45q^{23} - 2q^{27} + 9q^{29} + 23q^{31} - 42q^{33} + 20q^{37} + 9q^{39} + 54q^{41} - 46q^{43} - 135q^{47} - 255q^{49} + 115q^{51} - 7q^{57} + 324q^{59} - 55q^{61} + 215q^{63} + 38q^{67} - 77q^{69} + 86q^{73} + 153q^{77} - 49q^{79} - 65q^{81} + 279q^{83} + 213q^{87} - 134q^{91} + 53q^{93} + 98q^{97} + 137q^{99} + O(q^{100}) \)

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.p.a \(4\) \(24.523\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(-3\) \(0\) \(1\) \(q+(\beta _{2}-\beta _{3})q^{3}+(-\beta _{1}+3\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
900.3.p.b \(4\) \(24.523\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(6\) \(0\) \(-8\) \(q+3\beta _{1}q^{3}+(-4\beta _{1}-\beta _{2})q^{7}+(-9+\cdots)q^{9}+\cdots\)
900.3.p.c \(12\) \(24.523\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-2\) \(0\) \(6\) \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6})q^{7}+\cdots\)
900.3.p.d \(16\) \(24.523\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-2\) \(0\) \(1\) \(q+(\beta _{1}-\beta _{4})q^{3}-\beta _{10}q^{7}+(1-\beta _{3}+\beta _{15})q^{9}+\cdots\)
900.3.p.e \(16\) \(24.523\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(2\) \(0\) \(-1\) \(q+(-\beta _{1}+\beta _{4})q^{3}+\beta _{10}q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)
900.3.p.f \(24\) \(24.523\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)