Properties

Label 900.3.f
Level $900$
Weight $3$
Character orbit 900.f
Rep. character $\chi_{900}(199,\cdot)$
Character field $\Q$
Dimension $88$
Newform subspaces $9$
Sturm bound $540$
Trace bound $26$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(540\)
Trace bound: \(26\)
Distinguishing \(T_p\): \(7\), \(29\)

Dimensions

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

Total New Old
Modular forms 384 92 292
Cusp forms 336 88 248
Eisenstein series 48 4 44

Trace form

\( 88q + 6q^{4} + O(q^{10}) \) \( 88q + 6q^{4} - 16q^{14} + 42q^{16} + 68q^{26} + 24q^{29} + 214q^{34} - 80q^{41} + 338q^{44} - 4q^{46} + 504q^{49} + 44q^{56} + 80q^{61} - 42q^{64} - 500q^{74} + 306q^{76} + 340q^{86} + 128q^{89} + 624q^{94} + O(q^{100}) \)

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.f.a \(2\) \(24.523\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-4q^{4}+4iq^{8}-5iq^{13}+2^{4}q^{16}+\cdots\)
900.3.f.b \(2\) \(24.523\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-4q^{4}-4iq^{8}-5iq^{13}+2^{4}q^{16}+\cdots\)
900.3.f.c \(4\) \(24.523\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(2+\zeta_{12}^{3})q^{4}+(-4\zeta_{12}+\cdots)q^{7}+\cdots\)
900.3.f.d \(8\) \(24.523\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(-1-\beta _{1})q^{4}+(-2\beta _{4}+2\beta _{7})q^{7}+\cdots\)
900.3.f.e \(8\) \(24.523\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}q^{2}+(1+\zeta_{20}^{4})q^{4}+(-3\zeta_{20}+\cdots)q^{7}+\cdots\)
900.3.f.f \(16\) \(24.523\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+(-1-\beta _{8})q^{4}+(-\beta _{11}-\beta _{13}+\cdots)q^{7}+\cdots\)
900.3.f.g \(16\) \(24.523\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{11}q^{7}+\cdots\)
900.3.f.h \(16\) \(24.523\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(1+\beta _{5})q^{4}+(\beta _{3}-\beta _{4}-\beta _{8}+\cdots)q^{7}+\cdots\)
900.3.f.i \(16\) \(24.523\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{10}q^{2}+(2-\beta _{5})q^{4}-\beta _{8}q^{7}+(2\beta _{10}+\cdots)q^{8}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)