Properties

Label 3450.2.d
Level $3450$
Weight $2$
Character orbit 3450.d
Rep. character $\chi_{3450}(2899,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $27$
Sturm bound $1440$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3450.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 27 \)
Sturm bound: \(1440\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3450, [\chi])\).

Total New Old
Modular forms 744 68 676
Cusp forms 696 68 628
Eisenstein series 48 0 48

Trace form

\( 68 q - 68 q^{4} + 4 q^{6} - 68 q^{9} + O(q^{10}) \) \( 68 q - 68 q^{4} + 4 q^{6} - 68 q^{9} + 68 q^{16} - 8 q^{19} + 8 q^{21} - 4 q^{24} + 24 q^{26} - 8 q^{29} - 24 q^{34} + 68 q^{36} - 8 q^{39} + 56 q^{41} + 8 q^{46} - 84 q^{49} - 4 q^{54} - 32 q^{59} + 64 q^{61} - 68 q^{64} - 8 q^{69} + 32 q^{71} - 24 q^{74} + 8 q^{76} + 16 q^{79} + 68 q^{81} - 8 q^{84} - 64 q^{86} - 40 q^{89} + 64 q^{91} - 16 q^{94} + 4 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3450, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3450.2.d.a $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{9}+\cdots\)
3450.2.d.b $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
3450.2.d.c $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
3450.2.d.d $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
3450.2.d.e $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{9}+\cdots\)
3450.2.d.f $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
3450.2.d.g $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
3450.2.d.h $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+5iq^{7}+\cdots\)
3450.2.d.i $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{9}+\cdots\)
3450.2.d.j $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
3450.2.d.k $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{7}+iq^{8}+\cdots\)
3450.2.d.l $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+5iq^{7}+\cdots\)
3450.2.d.m $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots\)
3450.2.d.n $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
3450.2.d.o $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
3450.2.d.p $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{7}+iq^{8}+\cdots\)
3450.2.d.q $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
3450.2.d.r $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
3450.2.d.s $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
3450.2.d.t $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
3450.2.d.u $2$ $27.548$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
3450.2.d.v $4$ $27.548$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
3450.2.d.w $4$ $27.548$ \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}-q^{6}-3\beta _{2}q^{7}+\cdots\)
3450.2.d.x $4$ $27.548$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}+q^{6}+2\beta _{2}q^{7}+\cdots\)
3450.2.d.y $4$ $27.548$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+q^{6}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
3450.2.d.z $4$ $27.548$ \(\Q(i, \sqrt{57})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+q^{6}-3\beta _{2}q^{7}+\cdots\)
3450.2.d.ba $6$ $27.548$ 6.0.181494784.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+\beta _{4}q^{3}-q^{4}-q^{6}-\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1725, [\chi])\)\(^{\oplus 2}\)