Properties

Label 900.3.l
Level $900$
Weight $3$
Character orbit 900.l
Rep. character $\chi_{900}(757,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $30$
Newform subspaces $8$
Sturm bound $540$
Trace bound $31$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 8 \)
Sturm bound: \(540\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 792 30 762
Cusp forms 648 30 618
Eisenstein series 144 0 144

Trace form

\( 30q - 2q^{7} + O(q^{10}) \) \( 30q - 2q^{7} + 8q^{11} + 6q^{13} - 38q^{17} - 86q^{23} + 36q^{31} + 54q^{37} + 104q^{41} + 126q^{43} - 78q^{47} - 214q^{53} + 124q^{61} + 190q^{67} + 52q^{71} + 182q^{73} - 340q^{77} - 366q^{83} + 588q^{91} - 90q^{97} + O(q^{100}) \)

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.l.a \(2\) \(24.523\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(14\) \(q+(7+7i)q^{7}-10q^{11}+(-9+9i)q^{13}+\cdots\)
900.3.l.b \(4\) \(24.523\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(-20\) \(q+(-5+5\beta _{1}+\beta _{2}-\beta _{3})q^{7}+(4+5\beta _{3})q^{11}+\cdots\)
900.3.l.c \(4\) \(24.523\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{7}-6q^{11}+5\beta _{3}q^{13}-6\beta _{1}q^{17}+\cdots\)
900.3.l.d \(4\) \(24.523\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+3\beta _{1}q^{7}-6q^{11}-5\beta _{3}q^{13}-18\beta _{1}q^{17}+\cdots\)
900.3.l.e \(4\) \(24.523\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+3\beta _{1}q^{7}+7\beta _{3}q^{13}+11\beta _{2}q^{19}+\cdots\)
900.3.l.f \(4\) \(24.523\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{7}-\beta _{3}q^{13}+26\beta _{2}q^{19}+46q^{31}+\cdots\)
900.3.l.g \(4\) \(24.523\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+4\beta _{1}q^{7}+15q^{11}-2\beta _{3}q^{13}-3\beta _{1}q^{17}+\cdots\)
900.3.l.h \(4\) \(24.523\) \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(4\) \(q+(1-\beta _{1})q^{7}-\beta _{3}q^{11}+(6+6\beta _{1})q^{13}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)