Properties

Label 2200.2.b
Level $2200$
Weight $2$
Character orbit 2200.b
Rep. character $\chi_{2200}(1849,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $13$
Sturm bound $720$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2200.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(720\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2200, [\chi])\).

Total New Old
Modular forms 384 46 338
Cusp forms 336 46 290
Eisenstein series 48 0 48

Trace form

\( 46 q - 42 q^{9} - 6 q^{11} + 16 q^{21} - 28 q^{29} - 16 q^{39} - 4 q^{41} - 30 q^{49} + 24 q^{51} + 20 q^{59} - 44 q^{61} - 20 q^{69} - 16 q^{71} + 40 q^{79} + 14 q^{81} - 52 q^{89} - 32 q^{91} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(2200, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2200.2.b.a 2200.b 5.b $2$ $17.567$ \(\Q(\sqrt{-1}) \) None 88.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{3}-2 i q^{7}-6 q^{9}-q^{11}+\cdots\)
2200.2.b.b 2200.b 5.b $2$ $17.567$ \(\Q(\sqrt{-1}) \) None 440.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{3}-i q^{7}-6 q^{9}-q^{11}-6 i q^{13}+\cdots\)
2200.2.b.c 2200.b 5.b $2$ $17.567$ \(\Q(\sqrt{-1}) \) None 440.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{7}+3 q^{9}-q^{11}-3\beta q^{13}+\cdots\)
2200.2.b.d 2200.b 5.b $2$ $17.567$ \(\Q(\sqrt{-1}) \) None 440.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{7}+3 q^{9}-q^{11}+8 q^{19}-4\beta q^{23}+\cdots\)
2200.2.b.e 2200.b 5.b $2$ $17.567$ \(\Q(\sqrt{-1}) \) None 440.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{7}+3 q^{9}+q^{11}+2\beta q^{13}-2\beta q^{17}+\cdots\)
2200.2.b.f 2200.b 5.b $4$ $17.567$ \(\Q(i, \sqrt{17})\) None 440.2.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2200.2.b.g 2200.b 5.b $4$ $17.567$ \(\Q(i, \sqrt{17})\) None 88.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2200.2.b.h 2200.b 5.b $4$ $17.567$ \(\Q(i, \sqrt{17})\) None 440.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2200.2.b.i 2200.b 5.b $4$ $17.567$ \(\Q(i, \sqrt{17})\) None 440.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+q^{11}+\cdots\)
2200.2.b.j 2200.b 5.b $4$ $17.567$ \(\Q(i, \sqrt{5})\) None 2200.2.a.n \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
2200.2.b.k 2200.b 5.b $4$ $17.567$ \(\Q(i, \sqrt{5})\) None 2200.2.a.p \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
2200.2.b.l 2200.b 5.b $6$ $17.567$ 6.0.44836416.1 None 2200.2.a.t \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{3}+(-\beta _{3}-\beta _{5})q^{7}+(-2+\cdots)q^{9}+\cdots\)
2200.2.b.m 2200.b 5.b $6$ $17.567$ 6.0.96668224.1 None 2200.2.a.u \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{4})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2200, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1100, [\chi])\)\(^{\oplus 2}\)