Properties

Label 1800.2.f
Level $1800$
Weight $2$
Character orbit 1800.f
Rep. character $\chi_{1800}(649,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $11$
Sturm bound $720$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(720\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1800, [\chi])\).

Total New Old
Modular forms 408 22 386
Cusp forms 312 22 290
Eisenstein series 96 0 96

Trace form

\( 22 q - 2 q^{11} - 10 q^{19} - 16 q^{29} - 4 q^{31} - 10 q^{41} - 6 q^{49} + 16 q^{59} + 4 q^{61} + 24 q^{71} + 20 q^{79} - 18 q^{89} + 24 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1800.2.f.a 1800.f 5.b $2$ $14.373$ \(\Q(\sqrt{-1}) \) None 40.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{7}-4 q^{11}-\beta q^{13}+\beta q^{17}+\cdots\)
1800.2.f.b 1800.f 5.b $2$ $14.373$ \(\Q(\sqrt{-1}) \) None 1800.2.a.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{7}-4 q^{11}+i q^{13}-4 i q^{17}+\cdots\)
1800.2.f.c 1800.f 5.b $2$ $14.373$ \(\Q(\sqrt{-1}) \) None 24.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-4 q^{11}-\beta q^{13}+\beta q^{17}+4 q^{19}+\cdots\)
1800.2.f.d 1800.f 5.b $2$ $14.373$ \(\Q(\sqrt{-1}) \) None 360.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{7}-2 q^{11}-2\beta q^{13}+\beta q^{17}+\cdots\)
1800.2.f.e 1800.f 5.b $2$ $14.373$ \(\Q(\sqrt{-1}) \) None 600.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{7}-2 q^{11}+3 i q^{13}-6 i q^{17}+\cdots\)
1800.2.f.f 1800.f 5.b $2$ $14.373$ \(\Q(\sqrt{-1}) \) None 200.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2 i q^{7}-q^{11}-4 i q^{13}-5 i q^{17}+\cdots\)
1800.2.f.g 1800.f 5.b $2$ $14.373$ \(\Q(\sqrt{-1}) \) None 120.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{7}+3\beta q^{13}+\beta q^{17}-4 q^{19}+\cdots\)
1800.2.f.h 1800.f 5.b $2$ $14.373$ \(\Q(\sqrt{-1}) \) None 360.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{7}+2 q^{11}-2\beta q^{13}-\beta q^{17}+\cdots\)
1800.2.f.i 1800.f 5.b $2$ $14.373$ \(\Q(\sqrt{-1}) \) None 1800.2.a.k \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{7}+4 q^{11}+i q^{13}+4 i q^{17}+\cdots\)
1800.2.f.j 1800.f 5.b $2$ $14.373$ \(\Q(\sqrt{-1}) \) None 120.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4 q^{11}-3\beta q^{13}+3\beta q^{17}+4 q^{19}+\cdots\)
1800.2.f.k 1800.f 5.b $2$ $14.373$ \(\Q(\sqrt{-1}) \) None 600.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+5 i q^{7}+6 q^{11}-3 i q^{13}-2 i q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1800, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)