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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1950.2.i.a 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.b 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.c 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.d 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.e 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.f 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.g 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.h 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.i 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.j 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.k 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.l 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.m 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.n 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.o 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.p 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.q 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.r 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.s 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.t 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.u 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.v 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.w 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.x 1950.i 13.c $2$ $15.571$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1950.2.i.y 1950.i 13.c $4$ $15.571$ \(\Q(\zeta_{12})\) None \(-2\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2})q^{3}+\cdots\)
1950.2.i.z 1950.i 13.c $4$ $15.571$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(-2\) \(-2\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
1950.2.i.ba 1950.i 13.c $4$ $15.571$ \(\Q(\sqrt{-3}, \sqrt{10})\) None \(-2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bb 1950.i 13.c $4$ $15.571$ \(\Q(\sqrt{-3}, \sqrt{11})\) None \(-2\) \(2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bc 1950.i 13.c $4$ $15.571$ \(\Q(\sqrt{-3}, \sqrt{10})\) None \(-2\) \(2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bd 1950.i 13.c $4$ $15.571$ \(\Q(\sqrt{-3}, \sqrt{10})\) None \(2\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.be 1950.i 13.c $4$ $15.571$ \(\Q(\sqrt{-3}, \sqrt{11})\) None \(2\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bf 1950.i 13.c $4$ $15.571$ \(\Q(\sqrt{-3}, \sqrt{10})\) None \(2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
1950.2.i.bg 1950.i 13.c $4$ $15.571$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(2\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{2}+(1-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
1950.2.i.bh 1950.i 13.c $4$ $15.571$ \(\Q(\zeta_{12})\) None \(2\) \(2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}^{2})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1950.2.i.bi 1950.i 13.c $4$ $15.571$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(2\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{2}+(1-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)