Properties

Label 2850.2.d
Level $2850$
Weight $2$
Character orbit 2850.d
Rep. character $\chi_{2850}(799,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $24$
Sturm bound $1200$
Trace bound $26$

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Defining parameters

Level: \( N \) \(=\) \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2850.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 24 \)
Sturm bound: \(1200\)
Trace bound: \(26\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2850, [\chi])\).

Total New Old
Modular forms 624 56 568
Cusp forms 576 56 520
Eisenstein series 48 0 48

Trace form

\( 56q - 56q^{4} + 4q^{6} - 56q^{9} + O(q^{10}) \) \( 56q - 56q^{4} + 4q^{6} - 56q^{9} + 8q^{11} + 56q^{16} - 4q^{19} - 4q^{24} + 24q^{26} + 8q^{29} - 40q^{31} - 8q^{34} + 56q^{36} + 16q^{39} + 40q^{41} - 8q^{44} - 16q^{46} - 24q^{49} - 32q^{51} - 4q^{54} + 64q^{59} - 8q^{61} - 56q^{64} + 32q^{69} - 64q^{71} - 56q^{74} + 4q^{76} + 40q^{79} + 56q^{81} + 16q^{86} + 40q^{89} + 96q^{91} + 48q^{94} + 4q^{96} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2850, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2850.2.d.a \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2850.2.d.b \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{9}+\cdots\)
2850.2.d.c \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2850.2.d.d \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2850.2.d.e \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2850.2.d.f \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
2850.2.d.g \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
2850.2.d.h \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
2850.2.d.i \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{9}+\cdots\)
2850.2.d.j \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.k \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
2850.2.d.l \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.m \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.n \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.o \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
2850.2.d.p \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
2850.2.d.q \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.r \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.s \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
2850.2.d.t \(2\) \(22.757\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
2850.2.d.u \(4\) \(22.757\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}-q^{4}-q^{6}+(\zeta_{12}+\cdots)q^{7}+\cdots\)
2850.2.d.v \(4\) \(22.757\) \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}-q^{6}+\beta _{2}q^{7}+\cdots\)
2850.2.d.w \(4\) \(22.757\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}+q^{6}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
2850.2.d.x \(4\) \(22.757\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}-q^{4}+q^{6}+(\zeta_{12}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)