Properties

Label 4410.2.a
Level $4410$
Weight $2$
Character orbit 4410.a
Rep. character $\chi_{4410}(1,\cdot)$
Character field $\Q$
Dimension $67$
Newform subspaces $53$
Sturm bound $2016$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4410.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 53 \)
Sturm bound: \(2016\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4410))\).

Total New Old
Modular forms 1072 67 1005
Cusp forms 945 67 878
Eisenstein series 127 0 127

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(26\)
Minus space\(-\)\(41\)

Trace form

\( 67q + q^{2} + 67q^{4} - q^{5} + q^{8} + O(q^{10}) \) \( 67q + q^{2} + 67q^{4} - q^{5} + q^{8} + q^{10} - 4q^{11} - 2q^{13} + 67q^{16} - 6q^{17} - 8q^{19} - q^{20} - 4q^{22} - 24q^{23} + 67q^{25} - 10q^{26} + 10q^{29} + 8q^{31} + q^{32} - 10q^{34} + 42q^{37} - 8q^{38} + q^{40} - 10q^{41} + 36q^{43} - 4q^{44} - 8q^{47} + q^{50} - 2q^{52} - 18q^{53} - 4q^{55} - 14q^{58} - 12q^{59} + 22q^{61} + 67q^{64} - 2q^{65} + 52q^{67} - 6q^{68} - 32q^{71} + 38q^{73} + 6q^{74} - 8q^{76} + 80q^{79} - q^{80} + 14q^{82} + 40q^{83} + 14q^{85} - 16q^{86} - 4q^{88} + 54q^{89} - 24q^{92} + 24q^{94} + 20q^{95} - 10q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4410))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 7
4410.2.a.a \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
4410.2.a.b \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
4410.2.a.c \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-3q^{11}+\cdots\)
4410.2.a.d \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-2q^{11}+\cdots\)
4410.2.a.e \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-2q^{11}+\cdots\)
4410.2.a.f \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-2q^{13}+\cdots\)
4410.2.a.g \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots\)
4410.2.a.h \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+2q^{11}+\cdots\)
4410.2.a.i \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+4q^{11}+\cdots\)
4410.2.a.j \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+5q^{11}+\cdots\)
4410.2.a.k \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+6q^{11}+\cdots\)
4410.2.a.l \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-4q^{11}+\cdots\)
4410.2.a.m \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-3q^{11}+\cdots\)
4410.2.a.n \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
4410.2.a.o \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
4410.2.a.p \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{13}+\cdots\)
4410.2.a.q \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{11}+\cdots\)
4410.2.a.r \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+2q^{11}+\cdots\)
4410.2.a.s \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+4q^{11}+\cdots\)
4410.2.a.t \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+4q^{11}+\cdots\)
4410.2.a.u \(1\) \(35.214\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+5q^{11}+\cdots\)
4410.2.a.v \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-6q^{11}+\cdots\)
4410.2.a.w \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-3q^{11}+\cdots\)
4410.2.a.x \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-3q^{11}+\cdots\)
4410.2.a.y \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-2q^{13}+\cdots\)
4410.2.a.z \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-2q^{13}+\cdots\)
4410.2.a.ba \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{11}+\cdots\)
4410.2.a.bb \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+2q^{11}+\cdots\)
4410.2.a.bc \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+4q^{11}+\cdots\)
4410.2.a.bd \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+6q^{11}+\cdots\)
4410.2.a.be \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-6q^{11}+\cdots\)
4410.2.a.bf \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-6q^{11}+\cdots\)
4410.2.a.bg \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-3q^{11}+\cdots\)
4410.2.a.bh \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-3q^{11}+\cdots\)
4410.2.a.bi \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-2q^{13}+\cdots\)
4410.2.a.bj \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots\)
4410.2.a.bk \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+2q^{11}+\cdots\)
4410.2.a.bl \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots\)
4410.2.a.bm \(1\) \(35.214\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+6q^{11}+\cdots\)
4410.2.a.bn \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bo \(2\) \(35.214\) \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bp \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+(2+\beta )q^{11}+\cdots\)
4410.2.a.bq \(2\) \(35.214\) \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.br \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bs \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+(2+\beta )q^{11}+\cdots\)
4410.2.a.bt \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bu \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bv \(2\) \(35.214\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(2+\beta )q^{11}+\cdots\)
4410.2.a.bw \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(2+3\beta )q^{11}+\cdots\)
4410.2.a.bx \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.by \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+(-2+\cdots)q^{11}+\cdots\)
4410.2.a.bz \(2\) \(35.214\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+(2+3\beta )q^{11}+\cdots\)
4410.2.a.ca \(2\) \(35.214\) \(\Q(\sqrt{7}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+(2+\beta )q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4410))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4410)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1470))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2205))\)\(^{\oplus 2}\)