Properties

Label 1950.2.i
Level $1950$
Weight $2$
Character orbit 1950.i
Rep. character $\chi_{1950}(451,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $92$
Newform subspaces $35$
Sturm bound $840$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 35 \)
Sturm bound: \(840\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1950, [\chi])\).

Total New Old
Modular forms 888 92 796
Cusp forms 792 92 700
Eisenstein series 96 0 96

Trace form

\( 92q - 2q^{2} - 46q^{4} + 4q^{8} - 46q^{9} + O(q^{10}) \) \( 92q - 2q^{2} - 46q^{4} + 4q^{8} - 46q^{9} + 10q^{13} - 16q^{14} - 46q^{16} + 2q^{17} + 4q^{18} - 12q^{19} + 16q^{21} + 8q^{22} - 16q^{23} + 26q^{26} - 18q^{29} - 48q^{31} - 2q^{32} + 4q^{33} + 44q^{34} - 46q^{36} - 26q^{37} + 8q^{39} - 2q^{41} + 4q^{42} - 8q^{43} - 8q^{46} - 32q^{47} - 66q^{49} + 32q^{51} + 4q^{52} - 52q^{53} + 8q^{56} + 8q^{57} + 14q^{58} - 16q^{59} - 6q^{61} + 16q^{62} + 92q^{64} + 8q^{66} + 16q^{67} + 2q^{68} - 12q^{69} - 40q^{71} - 2q^{72} + 100q^{73} - 2q^{74} - 12q^{76} - 16q^{78} + 8q^{79} - 46q^{81} + 22q^{82} - 48q^{83} - 8q^{84} - 48q^{86} + 20q^{87} + 8q^{88} + 52q^{89} - 20q^{91} + 32q^{92} + 8q^{94} + 28q^{97} - 10q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1950, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1950.2.i.a \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-5\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.b \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.c \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.d \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.e \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.f \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(3\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.g \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(4\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.h \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(4\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.i \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-5\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.j \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.k \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.l \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.m \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(2\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.n \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(2\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.o \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-3\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.p \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.q \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(1\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.r \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(1\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.s \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(2\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.t \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(-4\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.u \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(-4\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.v \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.w \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(2\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.x \(2\) \(15.571\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(5\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.y \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(-2\) \(-2\) \(0\) \(-2\) \(q+(-1+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2})q^{3}+\cdots\)
1950.2.i.z \(4\) \(15.571\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(-2\) \(-2\) \(0\) \(3\) \(q+(-1+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
1950.2.i.ba \(4\) \(15.571\) \(\Q(\sqrt{-3}, \sqrt{10})\) None \(-2\) \(2\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bb \(4\) \(15.571\) \(\Q(\sqrt{-3}, \sqrt{11})\) None \(-2\) \(2\) \(0\) \(2\) \(q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bc \(4\) \(15.571\) \(\Q(\sqrt{-3}, \sqrt{10})\) None \(-2\) \(2\) \(0\) \(4\) \(q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bd \(4\) \(15.571\) \(\Q(\sqrt{-3}, \sqrt{10})\) None \(2\) \(-2\) \(0\) \(-4\) \(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.be \(4\) \(15.571\) \(\Q(\sqrt{-3}, \sqrt{11})\) None \(2\) \(-2\) \(0\) \(-2\) \(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bf \(4\) \(15.571\) \(\Q(\sqrt{-3}, \sqrt{10})\) None \(2\) \(-2\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bg \(4\) \(15.571\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(2\) \(0\) \(-3\) \(q+(1-\beta _{2})q^{2}+(1-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
1950.2.i.bh \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(2\) \(2\) \(0\) \(2\) \(q+(1-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1950.2.i.bi \(4\) \(15.571\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(2\) \(0\) \(3\) \(q+(1-\beta _{2})q^{2}+(1-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)