Properties

Label 900.2.d
Level $900$
Weight $2$
Character orbit 900.d
Rep. character $\chi_{900}(649,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $360$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 900.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(360\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 216 8 208
Cusp forms 144 8 136
Eisenstein series 72 0 72

Trace form

\( 8 q - 12 q^{11} - 4 q^{19} + 4 q^{31} - 12 q^{41} + 12 q^{49} + 12 q^{59} + 4 q^{61} + 24 q^{71} - 16 q^{79} - 12 q^{89} - 4 q^{91}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
900.2.d.a 900.d 5.b $2$ $7.187$ \(\Q(\sqrt{-1}) \) None 300.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{7}-6 q^{11}+5 i q^{13}-6 i q^{17}+\cdots\)
900.2.d.b 900.d 5.b $2$ $7.187$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) 36.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2\beta q^{7}+\beta q^{13}-8 q^{19}-4 q^{31}+\cdots\)
900.2.d.c 900.d 5.b $2$ $7.187$ \(\Q(\sqrt{-1}) \) None 20.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{7}-\beta q^{13}+3\beta q^{17}+4 q^{19}+\cdots\)
900.2.d.d 900.d 5.b $2$ $7.187$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) 900.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+i q^{7}-7 i q^{13}+7 q^{19}+11 q^{31}+\cdots\)

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

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