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Properties

Label 2100.4.k
Level $2100$
Weight $4$
Character orbit 2100.k
Rep. character $\chi_{2100}(1849,\cdot)$
Character field $\Q$
Dimension $52$
Newform subspaces $17$
Sturm bound $1920$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2100.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(1920\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2100, [\chi])\).

Total New Old
Modular forms 1476 52 1424
Cusp forms 1404 52 1352
Eisenstein series 72 0 72

Trace form

\( 52 q - 468 q^{9} + O(q^{10}) \) \( 52 q - 468 q^{9} + 48 q^{19} - 84 q^{21} - 56 q^{29} + 432 q^{31} - 48 q^{39} + 696 q^{41} - 2548 q^{49} - 408 q^{51} + 112 q^{59} + 1560 q^{61} + 1248 q^{69} + 2384 q^{71} + 1456 q^{79} + 4212 q^{81} - 7768 q^{89} - 728 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2100.4.k.a 2100.k 5.b $2$ $123.904$ \(\Q(\sqrt{-1}) \) None 420.4.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3 i q^{3}-7 i q^{7}-9 q^{9}-44 q^{11}+\cdots\)
2100.4.k.b 2100.k 5.b $2$ $123.904$ \(\Q(\sqrt{-1}) \) None 420.4.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3 i q^{3}+7 i q^{7}-9 q^{9}-36 q^{11}+\cdots\)
2100.4.k.c 2100.k 5.b $2$ $123.904$ \(\Q(\sqrt{-1}) \) None 420.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{3}+7 i q^{7}-9 q^{9}-36 q^{11}+\cdots\)
2100.4.k.d 2100.k 5.b $2$ $123.904$ \(\Q(\sqrt{-1}) \) None 2100.4.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3 i q^{3}-7 i q^{7}-9 q^{9}-26 q^{11}+\cdots\)
2100.4.k.e 2100.k 5.b $2$ $123.904$ \(\Q(\sqrt{-1}) \) None 420.4.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3 i q^{3}+7 i q^{7}-9 q^{9}-16 q^{11}+\cdots\)
2100.4.k.f 2100.k 5.b $2$ $123.904$ \(\Q(\sqrt{-1}) \) None 2100.4.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{3}+7 i q^{7}-9 q^{9}-6 q^{11}+\cdots\)
2100.4.k.g 2100.k 5.b $2$ $123.904$ \(\Q(\sqrt{-1}) \) None 84.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{3}+7 i q^{7}-9 q^{9}+4 q^{11}+\cdots\)
2100.4.k.h 2100.k 5.b $2$ $123.904$ \(\Q(\sqrt{-1}) \) None 420.4.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3 i q^{3}+7 i q^{7}-9 q^{9}+32 q^{11}+\cdots\)
2100.4.k.i 2100.k 5.b $2$ $123.904$ \(\Q(\sqrt{-1}) \) None 420.4.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3 i q^{3}+7 i q^{7}-9 q^{9}+36 q^{11}+\cdots\)
2100.4.k.j 2100.k 5.b $2$ $123.904$ \(\Q(\sqrt{-1}) \) None 84.4.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 i q^{3}+7 i q^{7}-9 q^{9}+36 q^{11}+\cdots\)
2100.4.k.k 2100.k 5.b $4$ $123.904$ \(\Q(i, \sqrt{130})\) None 420.4.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}+7\beta _{1}q^{7}-9q^{9}-8q^{11}+\cdots\)
2100.4.k.l 2100.k 5.b $4$ $123.904$ \(\Q(i, \sqrt{421})\) None 420.4.a.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}-7\beta _{1}q^{7}-9q^{9}+(-6-\beta _{3})q^{11}+\cdots\)
2100.4.k.m 2100.k 5.b $4$ $123.904$ \(\Q(i, \sqrt{109})\) None 420.4.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3\beta _{1}q^{3}+7\beta _{1}q^{7}-9q^{9}+(6-\beta _{3})q^{11}+\cdots\)
2100.4.k.n 2100.k 5.b $4$ $123.904$ \(\Q(i, \sqrt{29})\) None 2100.4.a.p \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}-7\beta _{1}q^{7}-9q^{9}+(9+2\beta _{3})q^{11}+\cdots\)
2100.4.k.o 2100.k 5.b $4$ $123.904$ \(\Q(i, \sqrt{109})\) None 2100.4.a.q \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3\beta _{1}q^{3}+7\beta _{1}q^{7}-9q^{9}+(3^{3}-2\beta _{3})q^{11}+\cdots\)
2100.4.k.p 2100.k 5.b $6$ $123.904$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 2100.4.a.v \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}+7\beta _{1}q^{7}-9q^{9}+(-3-2\beta _{3}+\cdots)q^{11}+\cdots\)
2100.4.k.q 2100.k 5.b $6$ $123.904$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 2100.4.a.w \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}+7\beta _{1}q^{7}-9q^{9}+(2+\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2100, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)