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Properties

Label 900.2.n
Level $900$
Weight $2$
Character orbit 900.n
Rep. character $\chi_{900}(181,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $52$
Newform subspaces $4$
Sturm bound $360$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 900.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
Sturm bound: \(360\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(900, [\chi])\).

Total New Old
Modular forms 768 52 716
Cusp forms 672 52 620
Eisenstein series 96 0 96

Trace form

\( 52 q + 4 q^{5} + 6 q^{7} + O(q^{10}) \) \( 52 q + 4 q^{5} + 6 q^{7} - q^{11} - 6 q^{13} - 11 q^{17} + 4 q^{19} + 6 q^{23} + 4 q^{25} - 6 q^{29} - 7 q^{35} + 23 q^{37} - 7 q^{41} + 34 q^{43} + 39 q^{47} + 74 q^{49} + 9 q^{53} + 5 q^{55} + 27 q^{59} + 2 q^{61} + 28 q^{65} + 35 q^{67} + 19 q^{71} - 2 q^{73} + 20 q^{77} + 8 q^{79} + 36 q^{83} + 34 q^{85} + 32 q^{89} + 36 q^{91} + 14 q^{95} - 55 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
900.2.n.a 900.n 25.d $8$ $7.187$ \(\Q(\zeta_{15})\) None \(0\) \(0\) \(-5\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+2\zeta_{15}^{2}+\zeta_{15}^{3}+2\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{5}+\cdots\)
900.2.n.b 900.n 25.d $8$ $7.187$ 8.0.26265625.1 None \(0\) \(0\) \(5\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\beta _{3}-\beta _{6}-\beta _{7})q^{5}+(1+\beta _{2}+\beta _{6}+\cdots)q^{7}+\cdots\)
900.2.n.c 900.n 25.d $12$ $7.187$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+\beta _{4}-\beta _{5}+\beta _{6}+\beta _{7}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
900.2.n.d 900.n 25.d $24$ $7.187$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)