Properties

Label 1872.2.c
Level $1872$
Weight $2$
Character orbit 1872.c
Rep. character $\chi_{1872}(1585,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $12$
Sturm bound $672$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1872.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(672\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1872, [\chi])\).

Total New Old
Modular forms 360 36 324
Cusp forms 312 34 278
Eisenstein series 48 2 46

Trace form

\( 34 q + O(q^{10}) \) \( 34 q - 2 q^{13} + 4 q^{17} - 8 q^{23} - 34 q^{25} - 4 q^{35} - 4 q^{43} - 30 q^{49} + 8 q^{53} + 4 q^{61} + 12 q^{65} - 32 q^{77} - 48 q^{79} - 28 q^{91} + 24 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1872.2.c.a 1872.c 13.b $2$ $14.948$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+iq^{7}-2iq^{11}+(-3+i)q^{13}+\cdots\)
1872.2.c.b 1872.c 13.b $2$ $14.948$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}-iq^{7}+(-3+i)q^{13}+2q^{17}+\cdots\)
1872.2.c.c 1872.c 13.b $2$ $14.948$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{5}+\zeta_{6}q^{11}+(-1+\zeta_{6})q^{13}+\cdots\)
1872.2.c.d 1872.c 13.b $2$ $14.948$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{6}q^{7}+(-1-\zeta_{6})q^{13}+\zeta_{6}q^{19}+\cdots\)
1872.2.c.e 1872.c 13.b $2$ $14.948$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{7}+\zeta_{6}q^{11}+(-1-\zeta_{6})q^{13}+\cdots\)
1872.2.c.f 1872.c 13.b $2$ $14.948$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}-iq^{7}+(2+i)q^{13}-3q^{17}+\cdots\)
1872.2.c.g 1872.c 13.b $2$ $14.948$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}+iq^{11}+(3+i)q^{13}-2q^{17}+\cdots\)
1872.2.c.h 1872.c 13.b $2$ $14.948$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+2iq^{7}+3iq^{11}+(3+i)q^{13}+\cdots\)
1872.2.c.i 1872.c 13.b $2$ $14.948$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{5}-iq^{7}-iq^{11}+(3-i)q^{13}+\cdots\)
1872.2.c.j 1872.c 13.b $4$ $14.948$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(2\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
1872.2.c.k 1872.c 13.b $4$ $14.948$ 4.0.8112.1 \(\Q(\sqrt{-39}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{11}+\beta _{3}q^{13}+\cdots\)
1872.2.c.l 1872.c 13.b $8$ $14.948$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+\beta _{1}q^{7}+(\beta _{2}-\beta _{4})q^{11}+\beta _{5}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 2}\)