Properties

Label 7105.2.a
Level $7105$
Weight $2$
Character orbit 7105.a
Rep. character $\chi_{7105}(1,\cdot)$
Character field $\Q$
Dimension $384$
Newform subspaces $37$
Sturm bound $1680$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 7105 = 5 \cdot 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7105.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 37 \)
Sturm bound: \(1680\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7105))\).

Total New Old
Modular forms 856 384 472
Cusp forms 825 384 441
Eisenstein series 31 0 31

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

\(5\)\(7\)\(29\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(45\)
\(+\)\(+\)\(-\)\(-\)\(49\)
\(+\)\(-\)\(+\)\(-\)\(52\)
\(+\)\(-\)\(-\)\(+\)\(46\)
\(-\)\(+\)\(+\)\(-\)\(49\)
\(-\)\(+\)\(-\)\(+\)\(45\)
\(-\)\(-\)\(+\)\(+\)\(46\)
\(-\)\(-\)\(-\)\(-\)\(52\)
Plus space\(+\)\(182\)
Minus space\(-\)\(202\)

Trace form

\( 384 q - 2 q^{2} + 384 q^{4} - 8 q^{6} - 6 q^{8} + 376 q^{9} + O(q^{10}) \) \( 384 q - 2 q^{2} + 384 q^{4} - 8 q^{6} - 6 q^{8} + 376 q^{9} - 2 q^{10} - 4 q^{11} + 20 q^{12} + 16 q^{13} - 4 q^{15} + 392 q^{16} - 8 q^{17} + 26 q^{18} - 4 q^{19} + 8 q^{20} - 4 q^{23} - 8 q^{24} + 384 q^{25} + 12 q^{26} - 16 q^{30} + 12 q^{31} - 14 q^{32} - 24 q^{33} - 32 q^{34} + 384 q^{36} - 32 q^{37} + 8 q^{38} - 48 q^{39} - 18 q^{40} - 40 q^{41} - 48 q^{43} - 44 q^{44} - 8 q^{45} - 24 q^{46} + 80 q^{48} - 2 q^{50} + 32 q^{51} + 32 q^{52} + 8 q^{53} + 16 q^{55} - 48 q^{57} - 2 q^{58} - 16 q^{59} + 16 q^{60} + 16 q^{61} - 56 q^{62} + 376 q^{64} + 8 q^{65} + 8 q^{66} - 44 q^{67} - 76 q^{68} + 32 q^{69} + 24 q^{71} + 62 q^{72} + 12 q^{73} + 64 q^{74} - 20 q^{76} + 88 q^{78} - 36 q^{79} + 384 q^{81} + 28 q^{82} + 36 q^{83} - 20 q^{85} - 24 q^{86} + 12 q^{87} + 16 q^{88} + 16 q^{89} - 6 q^{90} + 92 q^{92} + 72 q^{93} + 96 q^{94} - 16 q^{95} - 64 q^{96} + 12 q^{97} - 164 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7105))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7 29
7105.2.a.a 7105.a 1.a $1$ $56.734$ \(\Q\) None 1015.2.a.a \(-1\) \(-2\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+3q^{8}+\cdots\)
7105.2.a.b 7105.a 1.a $1$ $56.734$ \(\Q\) None 145.2.a.a \(-1\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
7105.2.a.c 7105.a 1.a $1$ $56.734$ \(\Q\) None 1015.2.a.c \(0\) \(-1\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{5}-2q^{9}+6q^{11}+\cdots\)
7105.2.a.d 7105.a 1.a $1$ $56.734$ \(\Q\) None 1015.2.a.b \(0\) \(3\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{4}+q^{5}+6q^{9}-2q^{11}+\cdots\)
7105.2.a.e 7105.a 1.a $2$ $56.734$ \(\Q(\sqrt{2}) \) None 145.2.a.b \(-2\) \(4\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+2q^{3}+(1-2\beta )q^{4}+\cdots\)
7105.2.a.f 7105.a 1.a $2$ $56.734$ \(\Q(\sqrt{2}) \) None 7105.2.a.f \(0\) \(-2\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1-\beta )q^{3}-q^{5}+(-2-\beta )q^{6}+\cdots\)
7105.2.a.g 7105.a 1.a $2$ $56.734$ \(\Q(\sqrt{3}) \) None 1015.2.a.d \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+q^{5}-\beta q^{8}-3q^{9}+\beta q^{10}+\cdots\)
7105.2.a.h 7105.a 1.a $2$ $56.734$ \(\Q(\sqrt{2}) \) None 7105.2.a.f \(0\) \(2\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{3}+q^{5}+(2+\beta )q^{6}+\cdots\)
7105.2.a.i 7105.a 1.a $2$ $56.734$ \(\Q(\sqrt{17}) \) None 1015.2.a.e \(1\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-\beta )q^{3}+(2+\beta )q^{4}-q^{5}+\cdots\)
7105.2.a.j 7105.a 1.a $2$ $56.734$ \(\Q(\sqrt{2}) \) None 1015.2.i.a \(2\) \(0\) \(-2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2\beta q^{3}-q^{4}-q^{5}-2\beta q^{6}+\cdots\)
7105.2.a.k 7105.a 1.a $2$ $56.734$ \(\Q(\sqrt{2}) \) None 1015.2.i.a \(2\) \(0\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2\beta q^{3}-q^{4}+q^{5}+2\beta q^{6}+\cdots\)
7105.2.a.l 7105.a 1.a $3$ $56.734$ \(\Q(\zeta_{14})^+\) None 1015.2.a.f \(-3\) \(3\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
7105.2.a.m 7105.a 1.a $3$ $56.734$ \(\Q(\zeta_{14})^+\) None 1015.2.a.h \(-1\) \(-1\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
7105.2.a.n 7105.a 1.a $3$ $56.734$ \(\Q(\zeta_{14})^+\) None 1015.2.a.g \(-1\) \(1\) \(-3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
7105.2.a.o 7105.a 1.a $3$ $56.734$ 3.3.148.1 None 145.2.a.c \(1\) \(-2\) \(-3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
7105.2.a.p 7105.a 1.a $3$ $56.734$ 3.3.148.1 None 145.2.a.d \(3\) \(2\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
7105.2.a.q 7105.a 1.a $6$ $56.734$ 6.6.39505108.1 None 1015.2.a.i \(2\) \(-1\) \(6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{3}-\beta _{4})q^{4}+\cdots\)
7105.2.a.r 7105.a 1.a $7$ $56.734$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 1015.2.a.j \(-3\) \(-1\) \(7\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{6}q^{2}-\beta _{1}q^{3}+(1-\beta _{4}+\beta _{6})q^{4}+\cdots\)
7105.2.a.s 7105.a 1.a $7$ $56.734$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 1015.2.a.k \(3\) \(-1\) \(7\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7105.2.a.t 7105.a 1.a $8$ $56.734$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1015.2.a.l \(1\) \(-4\) \(-8\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
7105.2.a.u 7105.a 1.a $11$ $56.734$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 1015.2.a.m \(3\) \(-1\) \(-11\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
7105.2.a.v 7105.a 1.a $14$ $56.734$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 7105.2.a.v \(0\) \(-2\) \(14\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7105.2.a.w 7105.a 1.a $14$ $56.734$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 7105.2.a.v \(0\) \(2\) \(-14\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
7105.2.a.x 7105.a 1.a $14$ $56.734$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 7105.2.a.x \(2\) \(-6\) \(-14\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
7105.2.a.y 7105.a 1.a $14$ $56.734$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 7105.2.a.x \(2\) \(6\) \(14\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7105.2.a.z 7105.a 1.a $17$ $56.734$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 1015.2.i.c \(-6\) \(-7\) \(17\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7105.2.a.ba 7105.a 1.a $17$ $56.734$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 1015.2.i.c \(-6\) \(7\) \(-17\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
7105.2.a.bb 7105.a 1.a $17$ $56.734$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 1015.2.i.b \(-4\) \(-5\) \(17\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{16}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
7105.2.a.bc 7105.a 1.a $17$ $56.734$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 1015.2.i.b \(-4\) \(5\) \(-17\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{16}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
7105.2.a.bd 7105.a 1.a $19$ $56.734$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None 1015.2.i.d \(2\) \(-5\) \(-19\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{16}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
7105.2.a.be 7105.a 1.a $19$ $56.734$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None 1015.2.i.d \(2\) \(5\) \(19\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{16}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
7105.2.a.bf 7105.a 1.a $21$ $56.734$ None 1015.2.i.e \(6\) \(-7\) \(-21\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$
7105.2.a.bg 7105.a 1.a $21$ $56.734$ None 1015.2.i.e \(6\) \(7\) \(21\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$
7105.2.a.bh 7105.a 1.a $26$ $56.734$ None 7105.2.a.bh \(0\) \(-2\) \(-26\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$
7105.2.a.bi 7105.a 1.a $26$ $56.734$ None 7105.2.a.bh \(0\) \(2\) \(26\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$
7105.2.a.bj 7105.a 1.a $28$ $56.734$ None 7105.2.a.bj \(-4\) \(-12\) \(28\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$
7105.2.a.bk 7105.a 1.a $28$ $56.734$ None 7105.2.a.bj \(-4\) \(12\) \(-28\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7105))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7105)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(203))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1015))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1421))\)\(^{\oplus 2}\)