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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

\( 46 q - 42 q^{9} + O(q^{10}) \) \( 46 q - 42 q^{9} - 6 q^{11} + 16 q^{21} - 28 q^{29} - 16 q^{39} - 4 q^{41} - 30 q^{49} + 24 q^{51} + 20 q^{59} - 44 q^{61} - 20 q^{69} - 16 q^{71} + 40 q^{79} + 14 q^{81} - 52 q^{89} - 32 q^{91} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2200.2.b.a $2$ $17.567$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}-2iq^{7}-6q^{9}-q^{11}-6iq^{17}+\cdots\)
2200.2.b.b $2$ $17.567$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}-iq^{7}-6q^{9}-q^{11}-6iq^{13}+\cdots\)
2200.2.b.c $2$ $17.567$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+3q^{9}-q^{11}-3iq^{13}-3iq^{17}+\cdots\)
2200.2.b.d $2$ $17.567$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}+3q^{9}-q^{11}+8q^{19}-4iq^{23}+\cdots\)
2200.2.b.e $2$ $17.567$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}+3q^{9}+q^{11}+2iq^{13}-2iq^{17}+\cdots\)
2200.2.b.f $4$ $17.567$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2200.2.b.g $4$ $17.567$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2200.2.b.h $4$ $17.567$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2200.2.b.i $4$ $17.567$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+q^{11}+\cdots\)
2200.2.b.j $4$ $17.567$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
2200.2.b.k $4$ $17.567$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
2200.2.b.l $6$ $17.567$ 6.0.44836416.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{3}+(-\beta _{3}-\beta _{5})q^{7}+(-2+\cdots)q^{9}+\cdots\)
2200.2.b.m $6$ $17.567$ 6.0.96668224.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{4})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)

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

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