Properties

Label 1900.2.i
Level $1900$
Weight $2$
Character orbit 1900.i
Rep. character $\chi_{1900}(201,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $62$
Newform subspaces $7$
Sturm bound $600$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 7 \)
Sturm bound: \(600\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

Total New Old
Modular forms 636 62 574
Cusp forms 564 62 502
Eisenstein series 72 0 72

Trace form

\( 62 q + q^{3} + 4 q^{7} - 28 q^{9} + O(q^{10}) \) \( 62 q + q^{3} + 4 q^{7} - 28 q^{9} + 4 q^{11} - 7 q^{13} + q^{17} - 12 q^{19} - 6 q^{21} - 5 q^{23} - 2 q^{27} + 9 q^{29} + 12 q^{31} - 12 q^{33} + 36 q^{37} + 54 q^{39} + q^{41} - 17 q^{43} - 23 q^{47} + 78 q^{49} + 35 q^{51} - 13 q^{53} - 35 q^{57} + 11 q^{59} - 7 q^{61} - 6 q^{63} - 13 q^{67} - 34 q^{69} + 11 q^{71} + 13 q^{73} - 20 q^{77} + 13 q^{79} - 7 q^{81} + 20 q^{83} + 26 q^{87} + 7 q^{89} - 18 q^{91} + 19 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1900.2.i.a 1900.i 19.c $2$ $15.172$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{9}-4q^{11}+\cdots\)
1900.2.i.b 1900.i 19.c $2$ $15.172$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+4q^{7}-\zeta_{6}q^{9}-3q^{11}+\cdots\)
1900.2.i.c 1900.i 19.c $6$ $15.172$ 6.0.1783323.2 None \(0\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{3}+\beta _{5})q^{3}+(-1+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.d 1900.i 19.c $8$ $15.172$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}-\beta _{7}q^{7}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1900.2.i.e 1900.i 19.c $12$ $15.172$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{6})q^{3}+\beta _{4}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.f 1900.i 19.c $12$ $15.172$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}+\beta _{6})q^{3}-\beta _{4}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.g 1900.i 19.c $20$ $15.172$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{14}q^{3}+(\beta _{15}+\beta _{18})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)