Properties

Label 4400.2.b
Level $4400$
Weight $2$
Character orbit 4400.b
Rep. character $\chi_{4400}(4049,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $29$
Sturm bound $1440$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4400.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 29 \)
Sturm bound: \(1440\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4400, [\chi])\).

Total New Old
Modular forms 756 90 666
Cusp forms 684 90 594
Eisenstein series 72 0 72

Trace form

\( 90q - 90q^{9} + O(q^{10}) \) \( 90q - 90q^{9} + 6q^{11} - 16q^{19} + 16q^{21} - 12q^{29} + 4q^{31} + 4q^{41} - 90q^{49} + 16q^{51} - 52q^{59} - 52q^{61} + 16q^{69} - 12q^{71} - 40q^{79} + 42q^{81} - 4q^{89} + 64q^{91} - 18q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4400, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4400.2.b.a \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}-iq^{7}-6q^{9}+q^{11}+6iq^{13}+\cdots\)
4400.2.b.b \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}-2iq^{7}-6q^{9}+q^{11}+6iq^{17}+\cdots\)
4400.2.b.c \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}-q^{11}-2iq^{17}-4q^{19}+\cdots\)
4400.2.b.d \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}-q^{9}-q^{11}-3iq^{13}-4iq^{17}+\cdots\)
4400.2.b.e \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{3}-4iq^{7}-q^{9}+q^{11}+5iq^{13}+\cdots\)
4400.2.b.f \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-2iq^{7}-q^{9}+q^{11}-2iq^{13}+\cdots\)
4400.2.b.g \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-5iq^{7}+2q^{9}-q^{11}-2iq^{13}+\cdots\)
4400.2.b.h \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-2iq^{7}+2q^{9}-q^{11}+4iq^{13}+\cdots\)
4400.2.b.i \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+3iq^{7}+2q^{9}-q^{11}-6iq^{13}+\cdots\)
4400.2.b.j \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}+2q^{9}+q^{11}-2iq^{13}+\cdots\)
4400.2.b.k \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-2iq^{7}+2q^{9}+q^{11}+4iq^{13}+\cdots\)
4400.2.b.l \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}+3q^{9}-q^{11}-2iq^{13}+2iq^{17}+\cdots\)
4400.2.b.m \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}+3q^{9}+q^{11}-8q^{19}+4iq^{23}+\cdots\)
4400.2.b.n \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3q^{9}+q^{11}-iq^{13}+3iq^{17}-4q^{19}+\cdots\)
4400.2.b.o \(2\) \(35.134\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2iq^{7}+3q^{9}+q^{11}-3iq^{13}-3iq^{17}+\cdots\)
4400.2.b.p \(4\) \(35.134\) \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{1}q^{7}+(-6+\beta _{3})q^{9}+q^{11}+\cdots\)
4400.2.b.q \(4\) \(35.134\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}-\zeta_{8}q^{7}-5q^{9}-q^{11}+(-2\zeta_{8}+\cdots)q^{13}+\cdots\)
4400.2.b.r \(4\) \(35.134\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2})q^{7}+(-4+\cdots)q^{9}+\cdots\)
4400.2.b.s \(4\) \(35.134\) \(\Q(i, \sqrt{21})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{1}+3\beta _{2})q^{7}+(-3+\beta _{3})q^{9}+\cdots\)
4400.2.b.t \(4\) \(35.134\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{1}q^{7}+(-2+\beta _{3})q^{9}-q^{11}+\cdots\)
4400.2.b.u \(4\) \(35.134\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4400.2.b.v \(4\) \(35.134\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4400.2.b.w \(4\) \(35.134\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4400.2.b.x \(4\) \(35.134\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\)
4400.2.b.y \(4\) \(35.134\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{1}+3\beta _{2})q^{7}+(-1+\beta _{3})q^{9}+\cdots\)
4400.2.b.z \(4\) \(35.134\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
4400.2.b.ba \(4\) \(35.134\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
4400.2.b.bb \(6\) \(35.134\) 6.0.96668224.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{4})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)
4400.2.b.bc \(6\) \(35.134\) 6.0.44836416.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{3}+(-\beta _{3}-\beta _{5})q^{7}+(-2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2200, [\chi])\)\(^{\oplus 2}\)