Properties

Label 7056.2.b
Level $7056$
Weight $2$
Character orbit 7056.b
Rep. character $\chi_{7056}(1567,\cdot)$
Character field $\Q$
Dimension $100$
Newform subspaces $26$
Sturm bound $2688$
Trace bound $53$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7056.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(2688\)
Trace bound: \(53\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(19\), \(31\), \(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7056, [\chi])\).

Total New Old
Modular forms 1440 100 1340
Cusp forms 1248 100 1148
Eisenstein series 192 0 192

Trace form

\( 100q + O(q^{10}) \) \( 100q - 124q^{25} + 24q^{29} - 8q^{37} - 24q^{53} + 24q^{65} - 72q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(7056, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7056.2.b.a \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{6}q^{5}-2\zeta_{6}q^{11}-3\zeta_{6}q^{13}+4\zeta_{6}q^{17}+\cdots\)
7056.2.b.b \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{5}+\zeta_{6}q^{11}-3\zeta_{6}q^{17}-7q^{19}+\cdots\)
7056.2.b.c \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{13}-7q^{19}+5q^{25}+7q^{31}+\cdots\)
7056.2.b.d \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{6}q^{5}-2\zeta_{6}q^{11}-\zeta_{6}q^{13}-5q^{19}+\cdots\)
7056.2.b.e \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{5}+\zeta_{6}q^{11}+2\zeta_{6}q^{17}-2q^{19}+\cdots\)
7056.2.b.f \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{5}+3\zeta_{6}q^{11}+4\zeta_{6}q^{13}-2\zeta_{6}q^{17}+\cdots\)
7056.2.b.g \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-3\zeta_{6}q^{13}-q^{19}+5q^{25}-11q^{31}+\cdots\)
7056.2.b.h \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-3\zeta_{6}q^{13}+q^{19}+5q^{25}+11q^{31}+\cdots\)
7056.2.b.i \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{5}-\zeta_{6}q^{11}+2\zeta_{6}q^{17}+2q^{19}+\cdots\)
7056.2.b.j \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{5}-3\zeta_{6}q^{11}+4\zeta_{6}q^{13}-2\zeta_{6}q^{17}+\cdots\)
7056.2.b.k \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{6}q^{5}+2\zeta_{6}q^{11}-\zeta_{6}q^{13}+5q^{19}+\cdots\)
7056.2.b.l \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{6}q^{5}+2\zeta_{6}q^{11}-3\zeta_{6}q^{13}+4\zeta_{6}q^{17}+\cdots\)
7056.2.b.m \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{5}-\zeta_{6}q^{11}-3\zeta_{6}q^{17}+7q^{19}+\cdots\)
7056.2.b.n \(2\) \(56.342\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{13}+7q^{19}+5q^{25}-7q^{31}+\cdots\)
7056.2.b.o \(4\) \(56.342\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+\beta _{2}q^{11}+2\beta _{1}q^{13}-4q^{19}+\cdots\)
7056.2.b.p \(4\) \(56.342\) 4.0.2048.2 \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}+\beta _{3})q^{5}+(-2\beta _{1}-3\beta _{3})q^{13}+\cdots\)
7056.2.b.q \(4\) \(56.342\) 4.0.2048.2 \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{13}+(\beta _{1}-\beta _{2}+\cdots)q^{17}+\cdots\)
7056.2.b.r \(4\) \(56.342\) 4.0.2048.2 \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}+\beta _{3})q^{5}+(2\beta _{1}+3\beta _{3})q^{13}+\cdots\)
7056.2.b.s \(4\) \(56.342\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+\beta _{3}q^{11}+2\beta _{2}q^{13}+3\beta _{2}q^{17}+\cdots\)
7056.2.b.t \(4\) \(56.342\) 4.0.2048.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+(-2\beta _{1}+2\beta _{3})q^{11}+(2\beta _{1}+\cdots)q^{13}+\cdots\)
7056.2.b.u \(4\) \(56.342\) 4.0.2048.2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+(2\beta _{1}-2\beta _{3})q^{11}+(2\beta _{1}-\beta _{3})q^{13}+\cdots\)
7056.2.b.v \(4\) \(56.342\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+\beta _{2}q^{11}-2\beta _{1}q^{13}+4q^{19}+\cdots\)
7056.2.b.w \(8\) \(56.342\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{4}+\beta _{6})q^{5}+(-\beta _{2}-\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots\)
7056.2.b.x \(8\) \(56.342\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{4}+\beta _{6})q^{5}+(\beta _{2}+\beta _{4}-\beta _{6})q^{11}+\cdots\)
7056.2.b.y \(8\) \(56.342\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}-\beta _{4})q^{5}+(-\beta _{6}+\beta _{7})q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots\)
7056.2.b.z \(16\) \(56.342\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{15}q^{5}-\beta _{9}q^{11}+\beta _{8}q^{13}+(-2\beta _{6}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(7056, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7056, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2352, [\chi])\)\(^{\oplus 2}\)