Properties

Label 1850.2.b
Level $1850$
Weight $2$
Character orbit 1850.b
Rep. character $\chi_{1850}(149,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $16$
Sturm bound $570$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1850.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(570\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1850, [\chi])\).

Total New Old
Modular forms 298 54 244
Cusp forms 274 54 220
Eisenstein series 24 0 24

Trace form

\( 54 q - 54 q^{4} + 4 q^{6} - 78 q^{9} + O(q^{10}) \) \( 54 q - 54 q^{4} + 4 q^{6} - 78 q^{9} + 8 q^{11} + 54 q^{16} + 20 q^{19} + 8 q^{21} - 4 q^{24} + 4 q^{29} - 8 q^{31} + 78 q^{36} + 24 q^{39} + 8 q^{41} - 8 q^{44} + 24 q^{46} - 30 q^{49} - 28 q^{51} + 20 q^{54} + 8 q^{59} + 20 q^{61} - 54 q^{64} - 28 q^{66} + 72 q^{69} - 8 q^{71} + 10 q^{74} - 20 q^{76} + 16 q^{79} + 134 q^{81} - 8 q^{84} - 28 q^{86} + 32 q^{89} - 8 q^{91} + 24 q^{94} + 4 q^{96} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1850, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1850.2.b.a \(2\) \(14.772\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{8}+\cdots\)
1850.2.b.b \(2\) \(14.772\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+2iq^{7}+\cdots\)
1850.2.b.c \(2\) \(14.772\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{7}+\cdots\)
1850.2.b.d \(2\) \(14.772\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+3q^{9}-4q^{11}+\cdots\)
1850.2.b.e \(2\) \(14.772\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
1850.2.b.f \(2\) \(14.772\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-4iq^{7}+\cdots\)
1850.2.b.g \(2\) \(14.772\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)
1850.2.b.h \(2\) \(14.772\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{8}+\cdots\)
1850.2.b.i \(4\) \(14.772\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots\)
1850.2.b.j \(4\) \(14.772\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{6}-2\beta _{1}q^{7}+\cdots\)
1850.2.b.k \(4\) \(14.772\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+(1+\beta _{3})q^{6}+\cdots\)
1850.2.b.l \(4\) \(14.772\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
1850.2.b.m \(4\) \(14.772\) \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+2\beta _{2}q^{3}-q^{4}+2q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1850.2.b.n \(6\) \(14.772\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(\beta _{3}-\beta _{5})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots\)
1850.2.b.o \(6\) \(14.772\) 6.0.3182656.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{5}q^{7}+\cdots\)
1850.2.b.p \(6\) \(14.772\) 6.0.37161216.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 2}\)